If you can find a variety of other cats,from the small African wild cat,serval cats,caracal,cheetahs,leopards and lions then why not tigers.
A lion and a tiger can be similar but yet so different and by that i mean their social lifestyles are so different.
You could argue they came from the same ancestor but somehow lions just evolved to have a very complex social life unlike any other cats and extreme brutality that comes with it as they forge prides and territories.
Lions live a life full of constant warfare between each other as males fight for rule and territories and dire consequences for their young if males fail to defend their prides.
Did lions somehow evolve to be so violent due to the brutal African wild,that i don't know but it's a possibility.Think about it,there's dangerous prey everywhere and hyenas which live in social groups as well that can be extremely dangerous to lone lions.A lone lion in the African Savannah is as good as dead,and i personally believe a lone tiger would face the same fate and maybe that's why there aren't tigers.The first biggest threat to a lone tiger in the African Savannah would be a pride of lions,especially male lions defending territory,followed by hyenas that show no mercy to a lone cat!
My assumption is the reason other non-social cats have managed to survive is first of all the cheetah is the ferrari of land mammals and can outrun any danger and the leopard and smaller cats have the advantage of climbing trees to run for their lives,otherwise they would all be toast in the dangers that face every corner of the African wild.
Tigers for sure could not survive the African Savannah as huge and strong as they can get,the African wild is merciless and seems that the never ending wars in lion society has managed to make them the fighters from a land,where danger never sleeps.
Check out this documentary of the mighty 6 male lions of mapogo pride and it will blow your mind as far as the violent nature of lion society!
It's definitely not for the faint of heart,extremely graphic!