While using the pump action shotgun (I believe its called the MP133, not certain though) I noticed that to reload the weapon you must first empty the gun, either by firing all of the rounds or by removing them manually.
That is not how a shotgun works.
you should be able to add ammunition the shotgun at any point, regardless of whether it is partially full. That's how it works in reality.
Also with a real shotgun, once the first round is chambered an additional round can be added to the tube, meaning that in total the shotgun in-game should be able to hold 6 shells in the tube and one in the the chamber, for total of 7.
I have not tested whether this is the same case for the Repeater, but i believe this all applies to the Repeater as well(correct me if I'm wrong gun people, I've never owned a lever action personally).