Quarter-Finals! Sigma vs. Kuja

is it a valid move for sigma to deliberately destroy/collapse the entire cavern or erupt the lava and leave or sustain himself in wireframe form?

Destroy the cavern and leave? No. The idea is that the opponent must be defeated before an exit is provided to the victor. The arenas are inescapable, so that we don't have combatants pussing out and letting their surroundings do all the work for them.

That doesn't mean that the fighters can't use the arena to attack their opponent, but they can't just remove themselves from the fight and let the enviroment take care of the other person.