It is the infanticide after a productive male had been killed that inhibits the sustainability of prides.
When a new male joins a pride he invariably will kill the cubs in order to bring lionesses into oestrus again so he can produce his own bloodline offspring. To allow the sustainability of the best blood lines as well as hunting, males must never be shot until they are 7 years or older. In fact, taking an 8 year old male in a way preserves his memory and still good-looking pelt. After 8 years their condition will go down and many die of hunger.
Lions are the only big cats in the world that establish social structures. Prides typically consist of 4-5 adult lionesses, their dependent cubs, and a temporary coalition of family males - until the latter within moments can become enemies due to mating rights or the denial thereof. These males normally play a key role in defending their pride against invading males by forming coalitions of 2-3 individuals to defend the pride’s territory by roaring, patrolling, scent marking and aggressively attacking invading males.
Infanticide ensures that the new male will pass on his genes to boost his reproductive character while reducing the DNA of the previous dominant males. Trophy hunting over bait has by default killed the strongest male who had executed dominance over the bait, thereby allowing a lesser animal who would not have been able to fight him to kill his offspring and maybe mate with the lionesses in the pride
The social nature of lions and common employment of infanticide means that lion populations are greatly impacted by the loss of productive males. For example, after 72% of the adult males studied in Hwange National Park, Zimbabwe had been killed by trophy hunters when they roamed onto private land, these pride males were replaced by invading lion that caused high rates of infanticide and markedly disrupted population stability (Loveridge et al. 2007).
As a general rule, hunting males older than 7 years ensures the quantity as well as the quality of the population AND of the long-term huntability. The science of determining lions' age grew out of the need to make trophy hunting sustainable and therefor ethical. Determining a lions age is important for the ethical trophy hunter; I believe I can tell any lion's age to within a year.
Lion trophy hunting must be managed in a way that reduces directly related infanticide to achieve sustainable lion populations and long-term hunting. Sustainable trophy hunting can be accomplished by killing only adult males that have raised cubs to independence. This is exactly the reason for the excellent growth in lion populations on large private properties in South Africa.