Old English liðe "soft, mild, gentle, calm, meek," also, of persons, "gracious, kind, agreeable," from Proto-Germanic *linthja- (source also of Old Saxon lithi "soft, mild, gentle," Old High German lindi, German lind, Old Norse linr "soft to the touch, gentle, mild, agreeable," with characteristic loss of "n" before "th" in English), from PIE root *lento- "flexible" (source also of Latin lentus "flexible, pliant, slow," Sanskrit lithi).
In Middle English, used of the weather. Current sense of "easily flexible" is from c. 1300. Related: Litheness. Old and Middle English had the related verb lin "to cease doing (something)," also used of the wind dying down.