Thanks, but I don't think that Asiatic lions necessarily pushed out Caspian tigers, or restricted their range, because, even if Asiatic lions shared habitats with Caspian tigers, like with Bengal tigers, they would have still been used to different conditions. I can see that lions can tolerate the heat, like those in the Gir Forest and Kalahari Xeric Savannah, but tigers don't always tolerate the heat that well. Gir is said to be too hot or dry for the tigers, and even Siberian tigers may cool off in water when they feel too hot, and their habitat is cold, compared to Gir, Kalahari, and Tropical Asia, and humans reportedly drove lions to extinction in places like the Trans-Caucasus, before the tigers. Lions were apparently extinct there by the end of the 10th Century, whereas tigers were still there in the 20th Century.
Bengal tigress taking a dip in Ranthambore National Park, India:
Kalahari lion in the heat, Kgalagadi Transfrontier Park, South Africa: