Allow me. For all we know, DMC2 could've taken place years, even centuries, after 4. Dante is practically immortal from what we know so it would come to no surprise that Dante would look so young, and for all we know they could've meant 40 in demon years, which I would assume is 4 centuries, and even if this nonsensical theory isn't correct, lets just review the amount of crap Lady gets herself into for a mortal, It would come to me as no surprise if Lady, a mortal who nearly gets herself killed on a usual basis, was dead by the events of DMC2. Lady was one of Dante's friends since DMC3 when he was at his youngest in the canonical series, so wouldn't it make sense that he would be pretty god damn depressed over her death.
(I know the shippers would be depressed as hell)