Question: what do you do after you beat the psychic gym in pokemon x?
Answer: After you beat the Psychic Gym, you are supposed to receive word that Team Flare's lab is in Lumiose or however you spell it, this is confirmed by grunts outside of the gym, and learn that it's inside Lysandre Café. Go there, defeat the 2 people inside, and interact with the bookshelf in the back.