I've never hunted lion, and for what it costs to shoot one I probably never will. I know the .375 H & H Mag. has long been regarded as the quintessential lion cartridge. It's been around for about a century and has certainly proved itself. Further, it's the only cartridge to which J. H. Taylor devoted an entire chapter in his classic African Hunting Rifles and Cartridges, calling it the best all around African round.
Of course, when dealing with animals that bite back it's probably better to be over-gunned than under-gunned. I will, however, say that I have a Sako chambered in this round and find it a pleasure to shoot, even with hot loads pushing heavy bullets, and I'm no tough guy by any means. Anything much heavier hurts and might make me flinch. For my part I'd rather not get so stunned by the first shot that I'm late on a second shot if one is needed. That's why I think I'd go with my .375 if I ever gun for lion, which I almost certainly never will.