We all know that in the Sun&Moon Anime, Lille has a fear of Pokémon. Well, I have a little headcanon about how that fear came around...and it involves Ultra Beasts.
In Who'll Be in Charge of the Egg?(English tittle now known as Who's in Charge of the Egg?)
, we were shown were Lillie is staying. It's not at Kuikui's place's(to be fair, that's where Ash lives for now)
but instead, she lives in a private villa/mansion with a butler and maids. We also find out that her phobia of Pokémon is revealed to be the result of a traumatic experience involving her mother
that she doesn't remember. Now while this could be that Lusamine did something to Lillie to cause the traumatic experience and by extension the fear, it is just as likely that the traumatic experience was caused by an Ultra Beast.
A key thing to note is the fact Lillie lives in a villa currently. If the anime's version of Lusamine was as evil as her game counterpart, I don't think she would have let Lillie leave Aether Paradise, especially without her knowing about it. Unless she had to force off the island for reasons....(and no, I don't think we'll see Nebby anytime soon. They could go the same route they did with Squishy for Nebby though....)
Now, this poorly structured theory of mine relies on part of Lusamine's anime backstory being the same as the games. Lusamine and her husband Mohn start researching Ultra Wormholes, and then one day Mohn gets sucked up by one. Lusamine goes crazy trying to find him, preforming countless tests on Ultra Wormholes and by extension discovering Ultra Space and the Ultra Beasts, and here's where the theriy comes in. During one experiment, Lillie sneaks into the testing area. An Ultra Beast could have spontaisuly emerged from the portal, and being in an alien environment, freaks out and basically destroys everything, and badly hurts a few people in the progress......including Lillie. After she recovered, she can't remember much about the incident, but what she can remember mentally scars her and leaves her with a phobia of Pokémon. Lusamine would be broken from this since she thinks the Ultra Beasts and everything related to them have ruined her family(for note: taken her husband and hurt her daughter), she basically swears no mercy on them. This would also tie in to Type:Null being created, as a Ultra Beast Killer. Due to what Aether Paradise is....well, you can guess what would happen next. Due to her daughters new phobia, Lusamine wouldn't be able to keep Lillie around Aether Paradise, so she has Lille sent to Melemele Island where the villa is. (and the Pokémon School as well.)