When Volcano Hellion enters the battlefield, it triggers, dealing an arbitrarily large amount of damage to you and Volcano Hellion.
Instead of you losing the game as a state-based action, Lich's Mirror causes you to shuffle your hand, graveyard and all permanents you own into your library, causing Rhox Faithmender to phase in as The Moment leaves the battlefield, and causing you to gain life equal to twice the amount of damage dealt to you plus 40.