The story
From earlier lushious, lussyouse (“luscious, richly sweet, delicious”), a corruption of lustious, from lusty (“pleasant, delicious”) + -ous. Shakespeare uses both lush (short for lushious) and lusty in the same sense: "How lush and lusty the grass looks" (The Tempest ii. I.52). An alternative etymology connects luscious to a Middle English term: lucius, an alteration of licious, believed to be a shortening of delicious.
Etymology from Wiktionary, CC BY-SA 4.0.