First off, the African people are killing off the lions, and doing so without having even the slightest concern for conservation - there's simply no incentive to do so. Indigenous poachers and farmers are killing them off as they occupy habitat... This is the fault of "the west"?
Then along comes some "wealthy people" (I know one who makes $150k a year) who enjoy killing animals. They pay for their tags, guides, travel, and lodging, to kill a lion or kudu. Suddenly these troublesome beasts become a valuable resource - one, that if managed, can bring lots of capital and respect to an otherwise unappreciated resource. This makes for a promising and sustainable market, for people who must otherwise compete with US government subsidized food... This is certainly hard for most folks who see lions as animals you watch at the zoo.
One thing you do say that I completely agree with, however, is that we should leave the Africans alone. Let them manage their resources as they see fit. Most Americans dont live in homes with dirt floors, and most Africans dont see the Serengeti as a large zoo that was created for their viewing pleasure.