Historically guns made ranged combat more accessible to the untrained folk not the ones already highly trained. So a lever action rifle would likely make reloading faster and he has likely already spent the feats, class abilities, etc. on getting free reload.
If he built a lever action rifle it would be undeniably a better weapon than the currently available muskets. But we all know he wouldn't be happy with it since it wouldn't make his character any better.
Soo... my advice is not thinking in terms of what is best next historically. Either look at his character or ask him about what would be a gun that would make his character better. The answer is normally going to be some mechanical advantage that is replicating a magic ability of some kind. That's good. Base the improved weapon off that... prototype weapons SHOULD be expensive and keeping it inline with magic effects helps keep some semblance of balance in place.
Make sure you think about how you want it to stack (or not) with magic effects as well. Weapons are required to be masterwork to be made magical but the +1 to hit from being masterwork doesn't stack with the +1 to hit from being a +1 weapon. I would try to follow that same vein.
Anyway... that is my advice on it.