NegaiFreak
Plus Ultra!
I really hope Lillie doesn't overcome her fear this episode... that is far too early and needs to be used much later on in a more dramatic fashion.
I think it'll be more that she's comfortable to touch Vulpix as opposed to all of the other Pokémon around her. I do hope that it comes to a dramatic point later on, such as confronting her mother, but for now, let her at least touch Vulpix.
That alone should suffice.