DMC2 was never meant to be a DMC game. Before DMC1 was even completed, Production Studio 1 began making an action game starring a female character using the DMC engine. However, midway through DMC1's development, the amount of hype and attention it was getting garnered sequel production even before DMC1 came out. So they changed unnamed action game starring female character and labeled it DMC2. They added Dante, and development teams switched. Hideaki Itsuno - was brought on to the project late, to salvage what he could since the original director quit.
As you can tell, Lucia actually had the more fleshed out combo system, and the storyline had nothing to do with Dante or the DMC legacy, other than the mention that Dante is "the son of Sparda." When you actually look at it, the above statements make perfect sense. They shoehorned the DMC2 name on it because DMC1 was getting so much attention pre-release, and directors and designers switched midway through.
Source: Interviews, Hideki Kamiya's twitter, and me - all the little things I've picked up in the past 12 years of reading DMC related interviews, previews and shit like that.
