"turf, stretch of grass," 1540s, laune "glade, open space in a forest or between woods," from Middle English launde (c. 1300), from Old French lande "heath, moor, barren land; clearing" (12c.), from Gaulish (compare Breton lann "heath"), or from a cognate Germanic word, from Proto-Germanic *landam-, source of English land (n.). The -d perhaps was mistaken for an affix and dropped. Sense of "grassy ground kept mowed" first recorded 1733. Lawn-tennis is from 1884.
"thin linen or cotton cloth," early 15c., probably from Laon, city in northern France, a center of linen manufacture. The town name is Old French Lan, from Latin Laudunum, of Celtic origin. For form evolution, compare fawn (n.) from faon. Lawn sleeves (1630s) were emblematic of Anglican bishops.