No, lion hunting isn't illegal. But you are only allowed to hunt lions that are known to have killed humans.
When you show up in most african countries, you register your name and put a down payment towards hunting a lion. If they discover one that's near you, or you're next in line, you'll be called up to kill it.
My friend's father killed a huge lioness and then built a game room around it. Literally, it was too big to fit through the doors.