Apparently from a pre-Greek language; traditionally connected to Lydian labrys "double-edged axe," symbol of royal power, which fits with the theory that the original labyrinth was the royal Minoan palace on Crete. It thus would mean "palace of the double-axe." But Beekes finds this "speculative" and compares laura "narrow street, narrow passage, alley, quarter," also identified as a pre-Greek word. Used in English for "maze" early 15c., and in figurative sense of "confusing state of affairs" (1540s). As the name of a structure of the inner ear, the essential organ of hearing, from 1690s.
"red resinous substance," 1550s, perhaps immediately from French lacce, displacing or absorbing earlier lacca (early 15c.), from Medieval Latin lacca. All these are from Persian lak, from Hindi lakh (Prakrit lakkha), from Sanskrit laksha "red dye," which is of uncertain origin.
According to Klein, it means literally "one hundred thousand" and is a reference to the insects that gather in great numbers on the trees and create the resin. But others say lakh is perhaps an alteration of Sanskrit rakh, from an IE root word for "color, dye" [Watkins]. Still another guess is that Sanskrit laksha is related to English lax, lox "salmon," and the substance perhaps was so called from being somewhat the color of salmon [Barnhart]. Also see shellac (n.).
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.