I don't know anything about the strength of the Lee action, but in my Browning 71 I use Stars and Stripes ammo. Load some nice .348 WIN using tough jacketed Hawk bullets, 250 gr at 2350 FPS and 270 gr (SD .319) at 2150 FPS. Definitely enough for anything in North America. Possibly a reasonable choice for African plains game at moderate ranges while providing some cat insurance.

I agree, good quality bullets are necessary. Otherwise the conventional wisdom is always to go bigger/heavier in caliber. I have a Winny '86 in .50-110 WIN as well but I never feel undergunned with the 71.

Yeah I'm a rimmy and a leverhead...