I have researched this myself.
@wesheltonj encapsulated the definitions very well. So speaking specifically about South Africa, there is legal wild lion hunting that occurs every so often in the Greater Kruger area called the APNR, Associated Private Nature Reserves. These are typically baited hunts, CITES exportable and similar in cost to wild lion hunts in other African countries. The last one I was able to research in the APNR in 2018 cost approximately 60k. Also VERY politically sensitive. There is a private joke, if the lion has a “name” probably don’t kill it.
Then we have what you may be referring to, “wild managed lion” that reside in very small numbers in Private Big Five game reserves adjacent to the Greater Kruger. Researching how some of these lion are managed in these private reserves, the science involved and research papers, the various biological considerations have given me a headache.
These are not captive bred lion but they do live in a fenced Big Five Reserve. Only a very small number can be maintained. They do hunt and kill wild game present on the reserves hence the very small number of lion, just a few lion on one Big Five Reserve I know of. They are primarily there for tourism and not hunting.
It is seldom that one will be offered to hunt, nor do I fully understand yet how one could be legally exported to a CITES country like the U.S., I need to research this further. If I were given the opportunity to hunt a non exportable one I would if the cost weren’t prohibitive. My research reveals that a “problem” lion at one of these private Big Five reserves that needs to be removed will most likely be offered to a local hunter only, guided by a PH.
Then there is CBL-Captive Bred Lion in SA which has already been explained and I have no interest in hunting one.
I think the best bet for a lower priced wild lion hunt is a lioness hunt in Zimbabwe or Namibia, or a late season cancellation wild lion hunt in Zimbabwe if you are able to drop everything and go on short notice.