You sure about that?
There's another trailer showing Lillie dodging Lusamine's hug, which puts Lillie's reaction to Lusamine's hug in perspective. Is Lillie just embarrassed that Lusamine is doting on her like that, or is there's something deeper going on on Lillie's part? While we don't exactly know how Lusamine treated Lillie and Gladion in the games, what we can infer that she was overbearing on them. Since the anime takes place in an alternate earlier point in the story, we may just be seeing where the relation has strained for Lillie but not Lusamine. And of course you wonder if Lillie's phobia of touching Pokemon has to do with something Lusamine did.
Also we don't know if the Cosmog that Ash found (which isn't in the Aether Paradise, looks to be in Verdant Cavern) is Nebby. Nebby is the Cosmog that Lillie rescued from Aether Foundation, for all we know it only exists in the games. This Cosmog more seems friendly with Ash since he found it, Lillie also has Snowy so she doesn't really need a Nebby. Even if this Cosmog gets used in certain plot points similar to what Nebby went through, it's more just being used in place of Nebby (like how Ash always takes the place of the main character of that generation).
The fight between Solgaleo and Lunala is in a grainy filter so is probably just a "legend" being told to Ash & co.. Also note a recent poster only shows Solgaleo but not Lunala, plus another trailer shows the anime's alter is the Alter of the Moone. As it has done since Gen V, the anime seems to have made its own story using the elements of Sun & Moon. Looks like Solgaleo might have a big role, and probably the Cosmog that Ash has will become a Lunala. Also in the poster Ash has the new Z-Ring so there might be USUM stuff early on in "Alola Season 2" though I don't think anything it does would be reflective of what goes on in the game. Once again, we know that at the very beginning that Lillie's role is the same, and thoguh she may become a trainer I don't think it'll have any influence from the anime except maybe what Pokemon she'll have (we do need an Ice-type specialist...).
More Pokedex Info:
A Rotom Dex toy has revealed that Dusk Mane Necrozma is Alola #400 rather then #300 it was in Sun & Moon. So there seems to be just 200 new Pokemon + whatever Ultra Beasts they introduce.