"craving, longing, strong desire," 1796 [Grose], perhaps a back-formation from lecher, or deformed from a figurative use of latch (v.) in a secondary sense of "grasp, grasp on to." Or perhaps from letch (v.), a variant of leach.
lesson
lessor
lest
-let
let
letch
let-down
lethal
lethality
lethargic
lethargy