The Terror bird is hands down the best tame to use to clear the lava caves. Their gliding ability allows them to easily cross gaps with little worry of falling in. Good base stats for a cave runner terror bird is 2000 Hp and 300 melee. After imprinting pump Hp between 3000-5000 and pump the rest into melee.
Everyone seems to limit this to just being a "scout". If you get a high level (170+) the terror bird can easily be one of the most deadly mounts out there. It's speed is unmatched and its ability to glide from any height, if it has the stamina that is, makes it amazing. If you pump HP, speed, stamina, and later on movement speed, you will have an absolute killer. (WARNING: Even high level terror birds will have low weight, only bring your essentials to maximize on speed!)
Perfect mount to explore on the ground. Everyone uses a ptera to get around the map, but on the ground it's a whole different experience. Also this mount is my go to for cave exploring. 300+damage and 180+movement speed is a must.