late 13c., probably from Old English *læððe, variant of lætt "lath," apparently from a Proto-Germanic *laþþo (cf. Old Saxon, Old Norse latta, Middle Dutch, German latte "lath," Dutch lat, Middle High German lade "plank," which is source of German Laden "counter," hence, "shop"). As a verb, 1530s, from the noun.
"machine for turning," early 14c., of uncertain origin, probably from a Scandinavian source (cf. Danish drejelad "turning-lathe," Old Norse hlaða "pile of shavings under a lathe," related to hlaða "to load, lade").