There is still one thing I don't get regarding Lusamine, Lillie, and Aether Foundation.
Lusamine wants to have Cosmog back, and Lillie was last seen having Cosmog with her, so logically, Lusamine would have asked all her employees to look for the missing Lillie.
Yet prior to Aether House incident, Lillie was able to walk around most of Alola without any problem whatsoever, including Heahea City, despite the existence of an Aether branch office there. Lillie, having stayed in Aether Foundation for a longer time than Gladion, should have known Heahea City has an Aether branch, so she should have been more careful while she was there.
In fact, she didn't get caught until she decided to do something weird : choosing to stay in the Aether House, despite fully aware it belongs to Aether Foundation. Granted, it was Team Skull who kidnapped her, but why staying in Aether's location when there's a Pokemon Center nearby?
Also, if only they go to the regional professor's house to ask for help, they would've found Lillie (and by extension, Cosmog) right away