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.