As the storyline progresses, Lillie's Cosmog with the name of Nebby will once again evolve into Cover Legend of Pokemon Moon, Lunala. Eventually, Necrozma will capture and fuse with Lunala in order to turn into its Dawn Wings Form. it will then take things one step further by later reaching its Ultra Burst, thus turning into Ultra Necrozma. After defeating Necrozma in its Dawn Wings Form and later as Ultra Necrozma, you will ultimately save Lunala from Necrozma's hold.
After saving it,Lunala Lillie and Lusamine will take it back to the Aether Foundation to heal it, as it is very weak after being absorbed by Necrozma. However, after encountering Gladion at Mount Lanakila, he will mention how Lunala is now healed and how Lillie is back with Nebby on Mahalo Trail. When you go there, Lillie tells you that she thinks it's best for Lunala to travel with your player since she's not a trainer. You will then battle Lunala in hopes of capturing it.
Lunala will be at Level 60 for this battle, continuing to have its Shadow Shield Ability and being a Psychic/Ghost Type Pokemon. It will know the moves Moongeist Beam, Cosmic Power, Night Daze, and Shadow Ball.