Go to the fountain in the park, if you haven't done the fairy sidequest, then go to Shadowed Curios and buy the gold dubloon. Toss the dubloon into the fountain and a fairy will show up. Feed the fairy progressively larger fruit until she gives you the fairy dust. Go back to the fountain and offer to bring the fairy home. Go back to the fountain and see it is now an ice cream stand. Purchase the ice cream vat. Go to Lilly and the scenes should proceed as normal.