To include her in a future game doesn't mean including every playable person in past DMC's, though that would be like 5 people tops seeing as Vergil's dead and Sparda was replaced with Trishe. Besides it shouldn't be a bother if they were only extra skins like Trishe in DMC2. You can't tell me that wasn't a welcome addition. On another note, her play style would probably need some serious thought, but we've seen a heck load of what she can do in cut scene's and even gotten a chance to go toe-to-toe with her, and this was her at her weakest. On a fun level she gets a pass for me. She barely uses anything remotely bladed so I think going Bayonetta, gung ho, (without the heels) would work pretty well in this kind of game. Dante's gunslinger style wouldn't even compare.
Personally I like the idea of balancing. Lady for the ranged, Lucia for the melee and Dante being a mix of the two but with less mastery. If you aren't feeling the idea I understand, but for me personally I think it could work wonders.
Well, if Lady would be playable, people would start nagging about Trish needing to be playable, too. I don't think Lady is more popular than Trish, nor would she have more combo potential. It'd be fun, but maybe it'd only be possible in secret missions. That sounds like a better idea to me.