lacer is derived from laqs, a rope, a noose; and this comes from laqueus.
lacer: a lappet; applied to a margin with irregular, broad and deep emarginations, leaving lappet-like intervals.
early 13c., laz, "cord made of braided or interwoven strands of silk, etc.," from Old French laz "a net, noose, string, cord, snare" (Modern French lacs), from Vulgar Latin *lacium, from Latin laqueum (nominative laqueus) "noose, snare" (Italian laccio, Spanish lazo), a trapping and hunting term, probably from Italic base *laq- "to ensnare" (cf. Latin lacere "to entice"). Later also "net, noose, snare" (c.1300); "piece of cord used to draw together the edges of slits or openings in an article of clothing" (late 14c.). The "ornamental net pattern" meaning is first recorded 1550s. Sense of "cord for tying" remains in shoelace. As an adjective, lace-curtain "middle class" (or lower-class with middle-class pretensions) usually is used in reference to Irish-Americans, by 1928.
c.1200, "fasten (clothing, etc.) with laces and ties;" see lace (n.). Also "tighten (a garment) by pulling its laces" (early 14c.). To lace coffee, etc., with a dash of liquor (1670s) originally was used of sugar, and comes via the notion of "to ornament or trim." Related: Laced; lacing. Laced mutton was "an old word for a whore" [Johnson].