What do you think would have happened had the Permian extinction never occurred? It occurred at a time when mammal like reptiles, Gorgonopsians, Dycynodonts, and Cynodonts were at their height. The dinosaurs would probably still evolve, though they would probably be small animals, maybe they would evolve alongside them, and mammals would arise and rule until the asteroid hit the earth.
The asteroid would have hit regardless of the Permian extinction, so the only difference are the big animals that go extinct, probably large mammals, though a few tiny ones would survive.
If that occurred, then perhaps the dinosaurs would become the dominant species, but with the lower oxygen level, animals would probably be similar in size to the animals of today.
If the ancestors of primates survived, then perhaps humans would evolve, and become the dominant animal, though instead of lions, there'd be animals like Allosaurus or T-rex. Of course this is just a guess, as alternate history gets harder to predict the further back. What do you think?