I know it’s just a movie, but is it believable to think that Anakin could survive those burns even with the suit?
Well if we’re talking in the real world:
The burns, yes. Assuming there is proper medical attention it is possible and has happened to survive third degree burns on your entire body.
But the burns aren’t really what he’d have to worry about. He’d be dead (along with Obi wan mind you) long before that would even matter from breathing in the excrutiatingly hot, ashy, poisonous air around the lava.