Responses
I think it may possibly be hereditary. Her mother was the one to wish to go back, but she probably has some powers herself as they are of the same blood.
She doesn't only lily has, after all she is the chosen one
Is it possible for her to be the one to turn back the time and not her mother? Maybe in her last moment, she wishes for everything to turn back and she got her wishes, but instead of her keeping the memories, the person (mother) she wishes to get back is the one who keep it.