After reading the first chapter of Vampire Savior: Tamashii no Mayoigo yesterday, I noticed something VERY interesting - in most of the games where Darkstalkers characters end up crossing over, Morrigan is true to how she is in the games, but the only crossover game Lilith is true to her in-game series counterpart is in Marvel vs. Capcom: Clash of Super Heroes.

In all her other appearances in crossovers, Lilith is characterized as she is in the manga, with her wanting to stay separate from Morrigan. Some other crossovers & media portray Morrigan like her manga counterpart too, such as TEPPEN and the infamous UDON Darkstalkers comics. Adding onto THAT, the Darkstalkers OVA has Morrigan as more of a chaotic neutral character who - unlike in the games - is interested in Demitri.

Moral of the story? Adapting certain Darkstalkers characters (like Morrigan & Lilith) always ends up with VERY weird results. You could either make them accurate to the games (like the Capcom vs. series did), or you could just cut loose with them and characterize them however you'd like (see the manga).