Those "lizards"...
...were the nearest things to mammals back in the early Permian. Dimetrodon was a Synapsid, not a Lepidosaur (lizard), and close to the main evolutionary line to all mammals. By the end Permian the Synapsids had progressed to forms much closer to mammals, like the Therocephalians. In any event your ancestors would've probably have been the ones running around chasing other critters. The puzzle is just why some survived the Great Halocarbon Choke-Fest - like Lystrosaurus - and others bit the dust.