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I have negative 10 life, such as due to Platinum Angel and I play Lich. Lich says:
As Lich enters the battlefield, you lose life equal to your life total.
If you would gain life, draw that many cards instead.
Does playing Lich in this situation cause me to draw 10 cards (by means of causing me to gain 10 life and then replacing that with card draw)?
Nothing happens. You lose 0 life, which is the same as not losing any life. You don't draw cards.
I think what you're imagining is "losing negative ten life" = "gain 10 life". However, you cannot lose negative life.
107.1b Most of the time, the Magic game uses only positive numbers and zero. You can’t choose a negative number, deal negative damage, gain negative life, and so on. However, it’s possible for a game value, such as a creature’s power, to be less than zero. If a calculation or comparison needs to use a negative value, it does so. If a calculation that would determine the result of an effect yields a negative number, zero is used instead, unless that effect doubles or sets to a specific value a player’s life total or a creature’s power and/or toughness.
The first bolded section is pretty clear cut ("You can't [...] gain negative life") but the second part also explains the principle behind it. The principle is that when you're gaining life, you gain +number life, but the calculation sees you would gain -number life instead, so we replace the negative with 0: you gain 0 life.
The text on the image says "You lose all life. If you would gain life later in the game ..." Even if losing negative life were gaining life, it's not happening "later in the game". The oracle text that you quote consists of two different statements. The EtB effect happens as the spell is being resolved. The gaining life is a static ability of the enchantment, and only applies when the enchantment is already on the battlefield.
614.12, 614.16d. We now take into account what would exist if they were already on the battlefield, so that e.g. Endless One entering with Humility in play won't enter with its +1/+1 counters.
Jul 5, 2018 at 22:25