what happens to lily?

Harry did see his mother die - she did die! - but because he was so young at the time he didn't understand what had happened. To see thestrals, you don't just to have literally witnessed death. You need to have seen someone die, be old enough to understand what death is, and have it sunk in. That's why he didn't see them at the end of his fourth year either - Cedric's death hadn't sunk in yet.

Harry didn't see her die. She was outside guarding the door, where voldemort killed her. In his flashback of voldemort's memory in the 7th book, it said that harry was smiling and happy when he walked in the room, because he didn't see what happened. Hope this helped:)

Lily is murdered by Lord Voldemort, but at the time Harry was not old enough to understand death and remember it. By the time of Cedric's death he understood what had happened and the next year he could see the thestrals.