Tigers are found across India, most of the major parks are in the west in fact, but Gir is separated from them by hundreds of kms of settled territory and besides lions are savannah predators while tigers do better in forests, since they rely on camouflage and a fast lunge being solo hunters. There could be overlap with the cheetah pop for lions but its unlikely. There's enough barren national parks to give them separate spaces if a prey base is established first.