Etymology
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letch (n.)

"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.

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Definitions of letch

letch (n.)
man with strong sexual desires;
Synonyms: satyr / lecher / lech
From wordnet.princeton.edu