prefix of reversal, deprivation, or removal (as in unhand, undo, unbutton), Old English on-, un-, from Proto-Germanic *andi- (source also of Old Saxon ant-, Old Norse and-, Dutch ont-, Old High German ant-, German ent-, Gothic and- "against"), from PIE *anti "facing opposite, near, in front of, before, against" (from PIE root *ant- "front, forehead," with derivatives meaning "in front of, before").
More or less confused with un- (1) through similarity in the notions of "negation" and "reversal;" an adjective such as unlocked might represent "not locked" (un- (1)) or the past tense of unlock (un- (2)).
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].