I have three cats and a dog. I love my animals. That said, I have no problem killing pest animals like a squirrel or raccoon that is being destructive.
The laws regarding killing an animal, even under disgusting circumstances like those depicted in the OP, are not however the same as for killing a human being. This is a slippery slope, animals are butchered every day for our tables, raised under abhorrent conditions for the purpose of being killed and consumed.
So while I certainly agree that this form of "sport" has no place in a civilized society, I do not agree with those that feel that he should be beheaded for killing the lion.
You don't go to jail for running over a raccoon or smoking a deer with your car. The repercussions for hitting a human are markedly different. So in the case of beheading this lion, the repercussion also, are (suitably) different. We humanize our pets, we make them part of our family, but as far as wild fare goes, this lion is no different from a bear, deer or moose, animals that are hunted (usually for food) every year. So while this was indeed wasteful and disgusting, it is not in-line with killing somebody's pet, let alone killing another human being.