An Etymological Dictionary of the German Language/erlauben
erlauben, earlier erleuben, vb., ‘to allow, permit, grant,’ from MidHG. erlouben (erleuben), OHG. irlouben (irlouppen), ‘to allow’; comp. Goth. uslaubjan, ‘to permit, grant,’ AS. âlŷfan. The original meaning of erlauben, like that of glauben, is ‘to approve,’ which is also inherent in the Teut. root lub, upon which the word is based (comp. Lob, lieb, Glaube, which are connected by gradation of the root lub, liub, laub). An old abstract of erlauben appears in ModHG. Urlaub.