In regards effectiveness of larger bore cartridges in lever guns for end of barrel kills on cats, Kenneth Anderson, who slew quite a few maneater tigers and panthers (leopards) when operating out of Bangalore, Southern India, last century, used a '95 Winchester lever in 405 Win. Some of his kills were within feet of the end of his barrel after he had to rapidly work the lever to get off the final killing shot.
Kenneth's son, Donald, also hunted and dispatched quite a few cats including a leopard famously caught on film as it charged him from ambush. He was a left hander using a Mauser 10.75x68. Donald had set out after the problem leopard accompanied by a couple of his old school friends and walked past the animal hiding in the bush on the edge of a small clearing. He heard the leopard grunt and come for him. Fortunately the leopard came for him rather than his two unarmed friends, one the photographer, who were lagging behind Donald. First shot put it down but another needed to put its lights out. A cool headed shot in a close charge and then rapid reload with a bolt action for a left hander.