I was in a desert biome messing around with parrots, spawning loads in. I was right by a small pool of surface lava. One parrot started flying, then started flying over the lava pool. Half-way across, it stopped flying and slowly descended into the pool of lava, where it promptly died.

It seemed to me like a flying parrot does not avoid lava. As most other overworld mobs avoid lava like the plague, I'm guessing it should be trying to avoid lava.

It appears to avoid lava when not flying - this issue only occurs in flight.