Does skipping your draw step prevent you from losing to an empty library on that turn?

The rule that causes you to lose is CR 704.5b: a player who attempts to draw a card from an empty library loses the game. The key word is attempts — the loss is triggered by the act of drawing, not merely by having an empty library.

If your draw step is skipped (by an effect like Teferi's Puzzle Box interactions, Narset, Parter of Veils, or cards that explicitly say 'skip your draw step'), you simply do not draw during that step. Because no draw attempt is made, state-based action CR 704.5b never applies from that skipped draw step.

However, this only protects you from the draw-step draw itself. If anything else on that same turn causes you to draw a card — a spell, an ability, or any other effect — and your library is empty, you will still lose at that point. Skipping the draw step does not grant general immunity to losing from an empty library.

Example: You have Laboratory Maniac's replacement effect active... wait, let's use a clean example. You control a permanent that says 'skip your draw step' and your library is empty. During your draw step, nothing happens — no draw occurs, so 704.5b is never checked for a draw. You survive that turn. But if your opponent then plays an effect that forces you to draw a card, your empty library causes you to lose immediately.

In summary: skipping the draw step removes the draw attempt that would normally happen there (CR 500.7, CR 509), so you avoid the loss condition for that specific draw. The protection is narrow — it only covers the skipped draw, not any other draws that turn.