If you recall in Episode 8 when Ash visits Lillie's house with the Egg, you'll notice several stuffed animals. They would be Lapras, Pikachu, Clefairy and Eevee. Something tells me that her next Pokemon is going to be one of those 4 and since Lapras is a rider Pokemon owned by Lana and Ash has Pikachu, the only options that make sense are Clefairy and Eevee. Another possibility that came to mind is that instead of an Ice-type trainer, Lillie becomes a Fairy-type trainer. Ninetales is part Fairy, Eevee can evolve into Sylveon and Clefairy is a fairy type. Lillie would be one bad-ass trainer if that happens and would give reason for Lillie to pursue the Fairy Z-Crystal from Mina.