Is the selectable lichess puzzle difficulty (normal, difficult etc.) relative to your rating?

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The options are there for you to try. Easier option gives lower points rewards for correctly answered puzzles and greater deductions for incorrect ones. The opposite is true for hardest option. Just give them try.

Yes lockdownloz but if a 1000 player and 2000 player both choose normal difficulty, does the 2000 player get harder puzzles?

Sorry, I misunderstood your question; which is an interesting one. I think yes, the puzzles are determined by your puzzle rating. To find out for sure you would need to reset your puzzle rating; though that's not an option on here; unlike chess.com.

@chessfan124 I'm quite sure that yes. When I select "normal", I always get puzzles with a rating around my puzzle rating. When I select "easier", I always get puzzles around 300 points below my puzzle rating.

Yes.