Why can't someone use the Time Turner to go back and save Lilly James?

(1) It would not have worked back then because, with the altered time line, no one would know of the need to go back to prevent something that never happened.

(2) It would be difficult now, sixteen years later, because whoever does it would be stuck, lurking in the shadows, for sixteen years while normal time catches up with him. No one could sit still and watch all that happened without being tempted to tamper.

Mainly, such tampering would be undesirable because

(3) Voldemort would only try again, and most likely succeed, because Lilly would not always be there to stand in the way.

(4) In the unlikely event that Voldemort gave up and left the Potters alone, Harry would never have received that scar, which is the world's one and only chance of ending this nightmare. Saving James might be theoretically possible, but not worth the risk.

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P.S. On some other thread, I don't remember where, someone asked
why Dumbledore didn't attempt to kill Voldemort in the Ministry atrium (book 5).
Because he knew better. He began suspecting that Voldemort was using
horcruxes in the end of Harry's second year, and by the 5th book he was sure.