You can hunt practically any animal in Africa, including lions, all you have to do is pay the very high trophy fees. Last I heard, it was $1500 - $10,000 for a lion, depending on country, time etc. That's just the fee you have to pay for the pleasure of killing the animal, you have to pay the costs of the hunting trip on top.
The problem with hunting as a means of population control is that the hunters choose the largest, and therefore fittest, male lions they can, rather than the elderly and sick lions that nature would weed out.