In a Two-Headed Giant game, if your team would lose the game and you control Lich's Mirror, your team won't lose. Instead, you'll do what Lich's Mirror says and your teammate won't do anything. This is true even if the reason your team would lose is because your teammate tried to draw a card with an empty library or was affected by an ability that said they lost the game. Your life total (which is the same as your team's life total) becomes 20. Your team's life total is adjusted by the amount of life you gain or lose as a result of this, which basically means your team's life total becomes 20.