I always disliked the reloading animation of Lincoln's Repeater, I never really understood what was supposed to be happening. It's a great weapon, though, but far from my favourite unique small gun,
I never understood why LR is repaired by hunting rifles, yet uses .44 ammo. Also, the Backwater Rifle is the same basic model, yet uses 10mm ammo and crits like a sniper rifle.
The LR is more or less based on the Henry Rifle, which used a .44 caliber rimfire cartridge (.44 Magnum, OTOH, is a center fire cartridge). The rifle was fed by means of a tubular magazine mounted under the barrel - the reloading animation simulates that. You'd open the magazine near the muzzle, load your cartridges, close the magazine, rack the lever to chamber a round and fire the weapon.
The biggest thing about using hunting rifles to fix it, though, is that the LR is a lever action gun, while the hunting rifle is bolt action. The two would share absolutely no parts in common.