late 15c., according to The Middle English Compendium a variant of Middle English licius "delicious" (c. 1400), which is a shortening of delicious, with the variant form perhaps influenced by Old French luxure, lusure. But OED 2nd ed. and Century Dictionary are against all this and the former considers it "of obscure origin" while the latter suggests lusty with a pseudo-Latin ending. John Palsgrave, the 16c. grammarian, spelled it lussyouse. Related: Lusciously; lusciousness.
Earlier (1610s) as a kind of pear deemed especially luscious; in this sense the word is ultimately a Romanic folk-etymologization of Turkish beg-armudi "prince's pear" or "prince of pears," influenced in form by the place-name (probably not directly from the town name, because it is on the opposite end of the peninsula from where the pear grows). Also used of garden plants of the mint order with a smell like that of oil of bergamot (1843).