You can't lose the game.
Whenever you gain life, draw that many cards.
Whenever you lose life, for each 1 life you lost, exile a permanent you control or a card from your hand or graveyard.
When Lich's Mastery leaves the battlefield, you lose the game.
4/27/2018 While you can’t lose the game, your opponents can still win the game if an effect says so.
4/27/2018 While you control Lich’s Mastery, your life total still changes. Lich’s Mastery’s effects don’t replace the life gain or life loss.
4/27/2018 You don’t have to exile all the cards from one place. For example, if a source deals 5 damage to you, you may exile one permanent, two cards from hand, and two cards from your graveyard.
4/27/2018 If you run out of other permanents, cards in hand, and cards in graveyard, you’ll have to exile Lich’s Mastery itself and lose the game.
4/27/2018 If you’re dealt more damage than you have cards to exile, you’ll just exile everything you can.