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 Defiant Bloodlord to phase in as Oubliette leaves the battlefield, and setting your life total to 20.
Defiant Bloodlord triggers, causing an opponent to lose life equal to the life you gained.