mid-12c., forloren "disgraced, depraved," past participle of obsolete forlesan "be deprived of, lose, abandon," from Old English forleosan "to lose, abandon, let go; destroy, ruin," from for- "completely" + leosan "to lose" (from Proto-Germanic *lausa-, from PIE root *leu- "to loosen, divide, cut apart"). In the Mercian hymns, Latin perditionis is glossed by Old English forlorenisse. OED's examples of forlese end in 17c., but the past participle persisted. Sense of "forsaken, abandoned" is 1530s; that of "wretched, miserable" first recorded 1580s.
A common Germanic compound (cognates: Old Saxon farilosan, Old Frisian urliasa, Middle Dutch verliesen, Dutch verliezen, Old High German virliosan, German verlieren, Gothic fraliusan "to lose").
In English now often in forlorn hope (1570s), which is a partial translation of Dutch verloren hoop, in which hoop means "troop, band," literally "heap," and the sense of the whole phrase is of a suicide mission. The phrase more often than not is used in English as if it meant "a faint hope," and the misuse has colored the meaning of forlorn. Related: Forlornly; forlornness.
late 14c., resolucioun, "a breaking or reducing into parts; process of breaking up, dissolution," from Old French resolution (14c.) and directly from Latin resolutionem (nominative resolutio) "process of reducing things into simpler forms," noun of action from past participle stem of resolvere "to loosen" (see resolve (v.)).
From the notion of "process of resolving or reducing a non-material thing into simpler forms" (late 14c.) as a method of problem-solving comes the sense of "a solving" (as of mathematical problems), recorded by 1540s, as is that of "power of holding firmly, character of acting with a fixed purpose" (compare resolute (adj.)). The meaning "steadfastness of purpose" is by 1580s. The meaning "effect of an optical instrument in rendering component parts of objects distinguishable" is by 1860. In Middle English it also could mean "a paraphrase" (as a breaking up and rearranging of a text or translation).
In mid-15c. it also meant "frame of mind," often implying a pious or moral determination. By 1580s as "a statement upon some matter;" hence "formal decision or expression of a meeting or assembly," c. 1600. New Year's resolution in reference to a specific intention to better oneself is from at least the 1780s, and through 19c. they generally were of a pious nature.
Old English losian "be lost, perish," from los "destruction, loss," from Proto-Germanic *lausa- (source also of Old Norse los "the breaking up of an army;" Old English forleosan "to lose, destroy," Old Frisian forliasa, Old Saxon farliosan, Middle Dutch verliesen, Old High German firliosan, German verlieren, as well as English -less, loss, loose). The Germanic word is from PIE *leus-, an extended form of root *leu- "to loosen, divide, cut apart."
The verb also is merged with, or has taken the (weaker) sense of, the related Middle English leese "be deprived of, lose" (Old English leosan, a class II strong verb whose past participle loren survives in forlorn and love-lorn), from Proto-Germanic *leusanan (source also of Old High German virliosan, German verlieren, Old Frisian urliasa, Gothic fraliusan "to lose").
Hence lose in the transitive senses "part with accidentally, be deprived of, miss the possession or knowledge of" (money, blood, sleep, hair, etc.), c. 1200; "fail to keep, lose track of" (mid-13c.). Meaning "fail to preserve or maintain" is from mid-15c. Meaning "fail to gain or win" (something) is from c.1300; intransitive meaning "fail to win" (a game, contest, lawsuit, etc.) is from late 14c. Meaning "to cause (someone) to lose his way" is from 1640s; meaning "cease to have, be rid of" (something unwanted) is from 1660s.
To lose heart "become discouraged" is from 1744; to lose (one's) heart "fall in love" is from 1630s. To lose (one's) mind "become insane" is attested from c. 1500. To lose out "fail" is 1858, American English. To lose it "become distraught, break down and lose control of oneself" is by 1990s; the it probably being one's self-control or grip on reality. Related: Lost; losing.