Lily Potter was never Lily Potter, only James ever knew the truth that she was actually Tigerlily, the sister of Celestia and Luna. And instead of a son, they had a baby girl, Aurora. Upon Lily's death, Aurora was sent back to Equestria by Lily's secret plan when Voldemort tried to destroy her. Aurora is raised by Celestia and joins the Mane 6 as the Seventh Element of Harmony.
Lily Luna and her cousins and siblings go through their time at Hogwarts. Lily is close to her cousins Rose, Dominique, Roxane, and Lucy. But she feels like they over shadow her. It seems like they always have and always will.