Yours, Etc.: Origins and Uses of 8 Sign-Offs
c.1300, "absence, want; shortage, deficiency," perhaps from an unrecorded Old English *lac, or else borrowed from Middle Dutch lak "deficiency, fault;" in either case from Proto-Germanic *laka- (cf. Old Frisian lek "disadvantage, damage," Old Norse lakr "lacking"), from PIE *leg- "to dribble, trickle." Middle English also had lackless "without blame or fault."
late 12c., perhaps from Middle Dutch laken "to be wanting," from lak (n.) "deficiency, fault," or an unrecorded native cognate word (see lack (n.)). Related: Lacked; lacking.