Does drawing your last card immediately cause you to lose or do you lose when you try to draw again?

You do not lose the game simply by drawing your last card. Your library being empty is not itself a loss condition. You only lose when a game rule or effect instructs you to draw a card and your library has zero cards in it at that moment.

According to CR 104.3c, a player loses the game if they are required to draw a card from a library with no cards in it. The loss happens at the point the draw is attempted on an empty library — not at any earlier time.

State-based actions (CR 704.5b) check whether a player has an empty library, but only cause a loss when that player is required to draw. Specifically, CR 704.5b states that if a player attempted to draw a card from an empty library since the last time state-based actions were checked, that player loses. This means the loss is triggered by the draw attempt, not by the library becoming empty.

Concrete example: You have one card left in your library and draw it during your draw step — nothing bad happens. You play out your turn normally. On your next turn, when your draw step arrives and you attempt to draw again from your now-empty library, that draw attempt causes you to lose the game.

This distinction matters: effects that let you skip your draw step (like some Leylines) or replace your draw can save you from losing even with an empty library, because no illegal draw is ever attempted.