I've only lost one tamed Lox, to mosquitoes. But note that, for some reason, you can't use a Lox in combat.

Wild Lox: Easily 3-hits you and takes a dozen hits to kill. Has no trouble killing anything that annoys it.
Tame Lox: If you mount it, and charge into a Fuling, it instantly loses 1/3rd of its life, even before getting hit. Dies easily to mosquitoes. When an enemy approaches, it goes berserk and breaks its enclosure, then gets trivially killed by the enemies from which it was perfectly safe until it broke its enclosure.

Summary:
Taming Loxes is completely useless. If you want meat, just wander around the plains and kill wild ones; it's much faster and easier.

Note that you can feed tame Loxes Cloudberries, which sometimes restores their health to full. And sometimes it doesn't, just giving them +1.6 HP per interval, which is useless.