1560s, of unknown origin, perhaps related to Middle English lympen "to fall short" (c.1400), which is probably from Old English lemphealt "halting, lame, limping," which has a lone cognate in the rare Middle High German limphin, and perhaps is from a PIE root meaning "slack, loose, to hang down" (cognates: Sanskrit lambate "hangs down," Middle High German lampen "to hang down"). Related: Limped; limping. As a noun, 1818, from the verb.

1706, "flaccid, drooping," of obscure origin, perhaps related to limp, v..