Oh wait, you mean because Celestia got the infinite lives?
In Super Mario World 3, you can share your 1-ups with the other player. Who, if you're Mario, is your younger brother Luigi. That fit?
Immortal means you never die, not that you lived from the beginning of time.
Or, alternatively, she's immortal 'Highlander' style.
Either way, immortality didn't kick in until she was born, which was after the turtle park closed.