I once owned a lever action .30-30. I would have said that was more modern than a .44 lever action, but a little googling discovers there are still .44 lever action rifles being made that are even rigged for .44 magnum ammo.
On the gamey side of things, I'm okay with there only being a few ammo types as that has an effect on inventory space, but the lever action rifle being a .44 wouldn't add any ammo types.
Weird idea, what if a weapon mod let you change the weapon's ammo type? Yeh, it defies reality, but would it be an acceptable game thing?