Yes, the Zora armour makes you vulnerable to heat. Falling into lava wearing it gives you a gameover. Unless Link is, for some reason, wearing the Zora armour while fighting Batman, if Batman, somehow, tosses Link, who is physically superior to him in every way, and Links many tons of gear, into the lava, he's coming back out, mad. Worse, Batman is going in with him, since Link's grip is too strong for Batman to break.
Ice pellets in a room with a lava trench in it? I don't even know what you mean by tripping balls, bolas? Not strong enough to bind Link's feet together, he'd just snap the cord.
Batman is in a terrible position in this thread. He's on the opposite side of a lava trench from an enemy who is too durable for him to hurt, too heavy for him to move, and who happens to have a ranged weapon that can fire arrows hard enough to destroy diamonds. And none of his available gizmoes are of any use.
At range, Bats dies. Up close, Bats dies.