For your life total to become 1, you will gain or lose the appropriate amount of life. For example, if your life total is -4 when The Golden Throne's ability applies, it will cause you to gain 5 life. Alternatively, if your life total is 20 when it applies (perhaps because you tried to draw a card from an empty library), you will lose 19 life. Other cards that interact with life gain or life loss will interact with this effect accordingly. Notably, this means that if you can't gain life or the life gain event is modified by another replacement effect, you might still have 0 or less life and still lose the game.