An Etymological Dictionary of the German Language/Lug
Lug, m., Lüge, f., ‘lie, falsehood,’ from the equiv. MidHG. luc (g), lüge (lügene), OHG. lugin, f.; an abstract of lügen (dial. liegen), MidHG. liegen, OHG. liogan, str. vb. ‘to lie.’ Comp. OSax. lugina, ‘lie,’ from liogan, Du. leugen, logen, from liegen, AS. lyge (E. lie), from leógan, Goth. liugn, ‘lie,’ from liugan, str. vb. ‘to lie.’ —