Honestly, Lillie doesn't feel at all like her counterpart from the games imo. From what I've read she's living in a Mansion and even has a Butler whom Ash will battle in the next episode if I'm not mistaken, so I'm really at loss here as well. I mean, she COULD be hiding Cosmog, but it just doesn't seem likely at this point. Maybe she has yet to steal Cosmog and run away? Or maybe the anime is simply ditching the games and doing its own thing like it has done before.