Etymology
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shoe (n.)
Old English scoh "shoe," from Proto-Germanic *skokhaz (source also of Old Norse skor, Danish and Swedish sko, Old Frisian skoch, Old Saxon skoh, Middle Dutch scoe, Dutch schoen, Old High German scuoh, German Schuh, Gothic skoh). No known cognates outside Germanic, unless it somehow is connected with PIE root *skeu- "cover" (source also of second element in Latin ob-scurus).

Old plural form shoon lasted until 16c. Meaning "metal plate to protect a horse's hoof" is attested from late 14c. Distinction between shoe and boot (n.) is attested from c. 1400. To stand in someone's shoes "see things from his or her point of view" is attested from 1767. Old shoe as a type of something worthless is attested from late 14c.

Shoes tied to the fender of a newlywed couple's car preserves the old custom (mentioned from 1540s) of throwing an old shoe at or after someone to wish them luck. Perhaps the association is with dirtiness, on the "muck is luck" theory.
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shoe (v.)
Old English scogan "to shoe," from the root of shoe (n.). In reference to horses from c. 1200. Related: Shoed; shoeing.
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lace (n.)
early 13c., laz, "cord made of braided or interwoven strands of silk, etc.," from Old French laz "a net, noose, string, cord, tie, ribbon, or snare" (Modern French lacs), from Vulgar Latin *lacium, from Latin laqueum (nominative laqueus) "a noose, a snare" (source also of Italian laccio, Spanish lazo, English lasso), a trapping and hunting term, probably from Italic base *laq- "to ensnare" (compare Latin lacere "to entice").

Later also "net, noose, snare" (c. 1300); and "piece of cord used to draw together the edges of slits or openings in an article of clothing" (late 14c., as preserved in shoelace). In Middle English it mostly had the sense "cord, thread," especially for tying or binding. It was used of fishing lines and perhaps the gallows rope, crossbeams in architecture, and the net Vulcan used to catch Venus in adultery. Death's lace was the icy grip of Death, and Love's lace was a binding love.

From 1540s as "ornamental cord or braid," hence the meaning "fabric of fine threads in a patterned ornamental open net" (1550s), which soon became the main meaning of the English word. "Century Dictionary" (1902) describes by name 87 varieties. As an adjective, lace-curtain "middle class" (or lower-class with middle-class pretensions), often used in reference to Irish-Americans, is attested by 1928.
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lace (v.)
c. 1200, "fasten (clothing, etc.) with laces and ties," from Old French lacier "entwine, interlace, fasten with laces, lace on; entrap, ensnare," from laz "net, noose, string, cord" (see lace (n.)). From early 14c. as "tighten (a garment) by pulling its laces." From 1590s as "to adorn with lace;" the meaning "to intermix (coffee, etc.) with a dash of liquor" (1670s) originally also was used of sugar, and comes via the notion of "to ornament or trim," as with lace. Meaning "beat, lash, mark with the lash" is from 1590s, from the pattern of streaks. Related: Laced; lacing. Laced mutton was "an old word for a whore" [Johnson].
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snow-shoe (n.)
also snowshoe, 1670s, from snow (n.) + shoe (n.). Related: Snowshoes.
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lace-up (adj.)
1831, originally of boots, from the verbal phrase, from lace (v.) + up (adv.).
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lace-wing (n.)
also lacewing, type of insect, 1847; see lace (n.) + wing (n.). Earlier was lace-winged fly (1826), and the shorter for might be from this.
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shoe-shine (adj.)
1911, from shoe (n.) + shine (n.). One who shines shoes for money was a shoeblacker (1755).
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shoe-string (n.)
1610s, from shoe (n.) + string (n.). As figurative for "a small amount" it is recorded from 1882; as a type of necktie, from 1903; as a style of cooked potatoes from 1906.
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shoelace (n.)

also shoe-lace, 1640s, from shoe (n.) + lace (n.).An older word for the thong or lace of a shoe or boot was Middle English sho-thong, Old English scoh-þwang.

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