late 14c., "lattice, grating," from Old French trelis, trellis "trellis, fence," originally "sackcloth," from Vulgar Latin *trilicius, from Latin trilicis, genitive of trilix "having three threads, triple-twilled," from tri- (see tri-) + licium "thread," a word of unknown etymology.
Sense extended in Old French to things "woven" of iron, etc., which brought on influence of Old French treille "vine trellis," perhaps from Latin trichila "bower, arbor," which is apparently from Latin triclinium "couch extending round three sides of a table" (for reclining on at meals; from PIE root *klei- "to lean"). Meaning "lattice used to support growing vines" is from 1510s. As a verb, c. 1400. Related: Trellised.