Neat concept; tying the character's power to their remaining lives makes the gameplay feel desperate as you reach closer to Game Over while simultaneously acquiring more strength. Unfortunately, the game balance currently makes the earlier lives feel frustrating to play, as the character's movement and attack speed is very slow, the fire is very hard to hit, and in general the player will inevitably become overwhelmed by enemies. It also feels like all states are a no-win scenario for the player: the weakest state is far too slow and incapable of handling the horde of fire elementals (and is also the least fun to play), but the stronger spells cause collateral damage to the trees from the ice shrapnel (usually offscreen) that makes attacking the fire elementals seem like a bad idea (even though it's necessary to stave them off).
With some better balancing and stronger visual/audio feedback, I think the idea could be an interesting one!