As some have pointed out here, some countries have a .375 caliber minimum for dangerous game. However, if it's legal to use where you'll be hunting, the 9.3x62mm Mauser is a great choice. If you can find them, the 258gr RWS H-Mantel bullets for the 9.3 are an absolutely perfect choice for lion. They combine a perfect mix of rapid fragmentation with deep penetration. As an added bonus, they are designed to make clean, circular entrance and exit wounds that bleed freely, but do not ruin the hide.
http://thebiggamehuntingblog.com/2014/08/rws-h-mantel/
