Walkthrough: Just off Tapu Village on Route 15 is the Aether House, a location built by The Aether Foundation to further aid Pokemon. As you are led there from your Rotom Pokedex, you will have to save Lillie from a Team Skull Member who saw her bag move on its own and is damage for her to give him the Pokemon. It is up to you to stop him and send him running for the hills.
Team Skull Grunt - Level 33 Drowzee
After defeating him, Lillie will thank you with some Luxury Balls and Acerola will come and inform you that she's actually the next Island Captain (after you and Hau enter Aether House and Battle the Preschoolers looking for some fun). Her Island Trial is at the end of Route 14, and she'll be waiting for your arrival.