Online Etymology Dictionary

loden (n.): "coarse woolen cloth," 1880, from German loden "thick woolen cloth."
lodestar (n.): late 14c. (late 13c. as a surname), an old name for the pole star as the star that "leads the way" in navigation; from lode (n.) + star (n.). Figurative use from late 14c. Compare lodestone. Similar formation in Old Norse leiðarstjarna, German Leitstern, Danish ledestjerne.
lodestone (n.): "magnetically polarized oxide of iron," 1510s, literally "way-stone," from lode (n.) + stone (n.). So called because it was used to make compass magnets to guide mariners. Figurative use from 1570s. Compare lodestar.
lodge (n.): Middle English logge, mid-13c. in surnames and place names; late 13c. as "small building or hut," from Old French loge "arbor, covered walk; hut, cabin, grandstand at a tournament" (12c.), from Frankish *laubja "shelter" (cognate with Old High German louba "porch, gallery," German Laube "bower, arbor"), from Proto-Germanic *laubja- "shelter." On a widespread guess (backed by Watkins, OED) this likely originally meant "shelter of foliage," or "roof made from bark," and is from the same PIE root as leaf (n.).

Modern spelling is from c. 1500. The specific sense "hunter's cabin" is first recorded late 14c. Sense of "local branch of a society" is first recorded 1680s, of Freemasons, from an earlier use of lodge as "workshop of a group of masons" (mid-14c.). In the New World the word was used of certain American Indian buildings (1805), hence lodge-pole (1805) and lodge-pole pine (1859).
lodge (v.): c. 1200, loggen, "to encamp (an army), set up camp;" c. 1300 "furnish with a temporary habitation, put in a certain place," from Old French logier "to lodge; find lodging for" (12c., Modern French loger), from loge "hut, cabin" (see lodge (n.)).

From late 14c. as "to dwell, live; to have temporary accommodations; to provide (someone) with sleeping quarters; to get lodgings." Sense of "plant, implant, get (a spear, bullet, fist, etc.) in the intended place, to make something stick" is from 1610s. Meaning "deposit" (a complaint, etc.) with an official" is from 1708. Related: Lodged; lodging.
lodgement (n.): also lodgment, "act of lodging," 1590s, from French logement (14c.) "accommodation, lodgings," from Old French logier (see lodge (v.)).
lodger (n.): "one who lives in rented rooms in the house of another," 1590s, agent noun from lodge (v.). Earlier as "tent-dweller" (early 14c.); c. 1200 as a surname.
lodging (n.): early 14c., "encampment;" late 14c., "temporary accommodation; place of residence," verbal noun from lodge (v.). Related: Lodgings.
loess (n.): 1833 (in Lyell), "unstratified deposit of loam," a special use from 1823 by German mineralogist Karl Cäsar von Leonhard (1779-1862) of German Löss "yellowish-gray soil," of a type found in the Rhine valley, from Swiss German lösch (adj.) "loose" (compare German los, from Proto-Germanic *lausaz, from PIE root *leu- "to loosen, divide, cut apart." Related: Loessial.
loft (n.): "an upper chamber," c. 1300, an extended sense from late Old English loft "the sky; the sphere of the air," from Old Norse lopt (Scandinavian -pt- pronounced like -ft-) "air, sky," originally "upper story, loft, attic," from Proto-Germanic *luftuz "air, sky" (source also of Old English lyft, Dutch lucht, Old High German luft, German Luft, Gothic luftus "air").

If this is correct, the sense development would be from "loft, ceiling" to "sky, air." Buck suggests a further connection with Old High German louft "bark," louba "roof, attic," etc., with development from "bark" to "roof made of bark" to "ceiling," though this did not directly inform the meaning "air, sky" (compare lodge (n.)). But Watkins says this is "probably a separate Germanic root." Meaning "gallery in a church" first attested c. 1500. From 1520s as "apartment over a stable" used for hay storage, etc.
loft (v.): "to hit a ball high in the air," 1856, originally in golf, from loft (n.). Compare sky (v.) in the modern slang sense. An earlier sense was "to put a loft on" (a building), 1560s; also "to store (goods) in a loft" (1510s). Related: Lofted; lofting.
lofty (adj.): "exalted, of high rank," early 15c. (early 14c. as a surname); also "with a high purpose," from loft (n.) + -y (2). Literal sense of "high" is attested from 1580s. Related: Loftily; loftiness.
log (n.1): unshaped large piece of tree, early 14c., of unknown origin. Old Norse had lag "felled tree" (from stem of liggja "to lie," hence "a tree that lies prostrate"), but many etymologists deny on phonological grounds that this can be the root of English log. Instead, they suggest an independent formation meant to "express the notion of something massive by a word of appropriate sound" [OED, which compares clog (n.) in its original Middle English sense "lump of wood"].

Log cabin (1770) was the typical dwelling of the poor in antebellum U.S. history in the well-timbered region that was then the West. It has been a figure of the honest pioneer since the 1840 presidential campaign of William Henry Harrison (the original application was derisive and either way it was inaccurate). Falling off a log as a type of something easy to do is from 1839.
log (v.2): "to enter into a log-book," 1823, from log (n.2). Meaning "to attain (a speed) as noted in a log" is recorded by 1883. Meaning "to log in to a computer" is from 1963; it also sometimes is used to mean "log off" of a computer or program. Related: Logged; logging (n.2).
log (n.2): "record of observations, readings, etc.," originally "record of a ship's progress," 1842, sailor's shortening of log-book (1670s), the daily record of a ship's speed, progress, etc., which is from log (n.1) "piece of wood." The book so called because it recorded the speed measurements made by means of a weighted chip of a tree log on the end of a reeled log line (typically 150 to 200 fathoms). The log lay dead in the water, and sailors counted the time it took the line to play out. The line was marked by different numbers of knots, or colored rags, tied at regular intervals; hence the nautical measurement sense of knot (n.). Similar uses of the cognate word are continental Germanic and Scandinavian (such as German Log). General sense "any record of facts entered in order" is by 1913.
It [the log-book] is a journal of all important items happening on shipboard, contains the data from which the navigator determines his position by dead-reckoning ... and is, when properly kept, a complete meteorological journal. On board merchant ships the log is kept by the first officer: on board men-of-war, by the navigator. [Century Dictionary, 1897]
log (v.1): "to fell trees for logs," 1717; earlier "to strip a tree" to make it a log (1690s), from log (n.1). Related: Logged; logging (n.1).
log in (v.): verbal phrase, 1963 in the computing sense, from log (v.2) + in (adv.).
log-jam (n.): also logjam, "congestion of logs on a river," by 1851, American English; see log (n.1) + jam (n.2). The figurative sense is by 1890.
log-roll (v.): also logroll, 1835, a back-formation from log-rolling.
log-rolling (n.): also logrolling, in the legislative vote-trading sense, "mutual aid given in carrying out several schemes or gaining individual ends," 1823, American English, from the notion of neighbors on the frontier joining forces for rolling logs into heaps after the trees have been felled to clear the land (as in phrase you roll my log and I'll roll yours); see log (n.1) + verbal noun from roll (v.). "Sometimes many neighbors were invited to assist, and a merrymaking followed. [Century Dictionary]. In lumbering, in reference to rolling logs into a stream where they bound together and floated down to the mills.
LOG-ROLLING. 1. In the lumber regions of Maine it is customary for men of different logging camps to appoint days for helping each other in rolling the logs to the river, after they are felled and trimmed -- this rolling being about the hardest work incident to the business. Thus the men of three or four camps will unite, say on Monday, to roll for camp No. 1, -- on Tuesday for camp No. 2, -- on Wednesday for camp No. 3, -- and so on, through the whole number of camps within convenient distance of each other. [Bartlett]
However the phrase is not attested in any literal sense, only the political sense, until 1848.
loganberry (n.): 1893, American English, named for U.S. horticulturalist James H. Logan (1841-1928), who developed it by crossing a blackberry and a raspberry.
logarithm (n.): class of arithmetical functions used to shorten calculation, 1610s, logarithmus, coined in Modern Latin by Scottish mathematician John Napier (1550-1617), literally "ratio-number," from Greek logos "proportion, ratio, word" (see Logos) + arithmos "number" (from PIE *erei-dhmo-, suffixed variant form of root *re- "to reason, count"). Napier invented them and published a table in 1614; the kind chiefly in use were invented by his contemporary Henry Briggs, a professor of geometry at Gresham College, London.
logarithmic (adj.): "of, pertaining to, or consisting of logarithms," 1690s, from logarithm + -ic. Related: Logarithmical (1630s); logarithmetical (1620s).
logged (adj.): c. 1820, "reduced to the condition of a log" (n.1), which was old sailors' slang for an incapacitated wooden ship; thus "inert in the water."
logger (n.2): "one who enters data in a log," 1958, agent noun from log (v.2).
logger (n.1): "one who fells or cuts trees, one employed in getting out timber from forests," by 1708, agent noun from log (v.1).
loggerhead (n.): 1580s, "stupid person, blockhead, dunce, numbskull," perhaps from dialectal logger "heavy block of wood" + head (n.). Later it meant a type of thick-headed iron tool (1680s), a type of cannon shot, a post in the stern of a whale-boat, and a type of turtle (1650s). Loggerheads "fighting, fisticuffs" is from 1670s, but the exact notion in the compound is uncertain, perhaps it suggests the heavy tool used as a weapon. The phrase at loggerheads "in disagreement" is first recorded 1670s.
[W]e three loggerheads be: a sentence frequently written under two heads, and the reader by repeating it makes himself the third. [Grose, "Dictionary of the Vulgar Tongue," 1785]
loggia (n.): "roofed galley used as an open-air room," properly at a height of one or more stories, 1742, from Italian loggia, from French loge (see lodge (n.)).
logging (n.1): "act of felling timber," 1706, verbal noun from log (v.1).
logging (n.2): "act of recording in a log," 1941, verbal noun from log (v.2).
loggy (adj.): "heavy, sluggish," 1847; see logy. Related: Logginess.
logic (n.): mid-14c., logike, "branch of philosophy that treats of forms of thinking, science of distinction of true from false reasoning," from Old French logique (13c.), from Latin (ars) logica "logic," from Greek (he) logike (techne) "(the) reasoning (art)," from fem. of logikos "pertaining to speaking or reasoning" (also "of or pertaining to speech"), from logos "reason, idea, word" (see Logos). Formerly also logick. Sometimes formerly plural, as in ethics, but this is not usual. Meaning "logical argumentation" is from c. 1600. Contemptuous logic-chopper "sophist, person who uses subtle distinctions in argument" is from 1846.
logical (adj.): early 15c., "based on reason, according to the principles of logic," from logic + -al (1). Meaning "pertaining to logic" is c. 1500. Attested from 1860 as "following as a reasonable consequence." Related: Logically. Logical positivism, in reference to the ideas of the Vienna Circle of philosophers, is from 1931.
logician (n.): "person skilled in logic," late 14c., from Old French logicien (13c.), from logique (see logic). The Greek word was logistes.
login (n.): in the computer sense, as one word, by 1983, from the verbal phrase; see log in.
logistic (adj.): "pertaining to logic," 1620s, from Medieval Latin logisticus, from Greek logistikos "skilled in calculating; endued with reason," from logistes "a calculator," from logos "calculation, proportion" (see Logos). Related: Logistical (1560s); logistically. Logistics, from this word, in the sense "art of arithmetical calculation" is from 1650s.
logistics (n.): "art of moving, quartering, and supplying troops," 1846, from French (l'art) logistique "(art) of quartering troops," which apparently is from Middle French logis "lodging" (from Old French logeiz "shelter for an army, encampment," from loge; see lodge (n.)) + Greek-derived suffix -istique (see -istic). The form in French was influenced by logistique, from the Latin source of English logistic. Related: Logistical.
logo (n.): "simple symbol or graphic meant to represent something," 1937, probably a shortening of logogram "sign or character representing a word."
logo-: before vowels log-, word-forming element meaning "speech, word," also "reason," from Greek logos "word, discourse; reason," from PIE root *leg- (1) "to collect, gather," with derivatives meaning "to speak (to 'pick out words')."
logocentric (adj.): "centered on reason," 1931, from logo- "reason" + -centric.
logocracy (n.): "system of government in which words are the ruling powers," 1804; see logo- + -cracy "rule or government by." Popularized by Washington Irving.
In this country [America] every man adopts some particular slang-whanger as the standard of his judgment, and reads everything he writes, if he reads nothing else: which is doubtless the reason why the people of this logocracy are so marvellously enlightened. [Irving, "Salmagundi," 1821]
logogram (n.): "word-sign, sign or character representing a word," 1840, from logo- "word" + -gram. Generically, "any symbol representing graphically a product, idea, etc.," from 1966. The earliest use of the word (1820) is in the sense "logograph," but OED explains this as a substitute for logograph, "which in this sense is itself a mistake for logogriph," the old type of word-puzzle.
logograph (n.): "instrument for giving a graphic representation of speech, word-writer," 1879, from logo- "word" + -graph "instrument for recording; something written." Earliest use (1797) is in the sense "logogriph," and it frequently was used in place of that word (see logogriph). In ancient Greek, logographos was "prose-writer, chronicler, speech-writer." Related: Logographic.
logogriph (n.): type of word puzzle based on synonyms, etc., and often in the form of a verse, 1590s, from French logogriphe, from Greek logos "word" (see Logos) + gripos/griphos "riddle," a figurative use, literally "fishing basket, creel," probably from a pre-Greek word in a lost Mediterranean language. "The variation [p/ph] is typical for Pre-Greek words; such an origin for a fisherman's word is quite understandable" [Beekes].
logolatry (n.): "worship of words," 1810 (Coleridge), from logo- + -latry.
logomachy (n.): "contention about, or with, words," 1560s, a nativized Latinized form of New Testament Greek logomakhia "a war about words," from logomakhos (see logo- + -machy). Related: Logomach; logomachical.
logomaniac (n.): "one mad for words," 1870; see logo- "word" + -mania.
logon: in computer sense, as one word, by 1975, from log (v.2) + on (adv.).
logophobia (n.): "fear of words," 1890; see logo- "word" + -phobia "fear." Related: Logophobe; logophobic.
logopoeia (n.): a quality in poetic writing that charges words with meaning based on context and prior usage, a term introduced, along with phanopoeia (visual image) and melopoeia (sound), by Ezra Pound from Greek logopoeia, from logos "word" (see Logos) + poiein "to make, create" (see poet).
[T]he good writer chooses his words for their 'meaning,' but that meaning is not a set, cut-off thing like the move of knight or pawn on a chess-board. It comes up with roots, with associations, with how and where the word is familiarly used, or where it has been used brilliantly or memorably.

You can hardly say 'incarnadine' without one or more of your auditors thinking of a particular line of verse. [Pound, "ABC of Reading," 1934]