LUKE: I am going to the diner, I am going to get us some edible food and I’m gonna bring it back here for us to eat.
LORELAI: That is so not the point of today. I made this. I am insulted. I will now proceed to pout.
LUKE: I’ll bring back some brownies.
LORELAI: Ooh, the pouting has left the building.
Lorelai is referencing the phrase, “Elvis has left the building”. It’s a phrase that was often used by announcers at the end of Elvis Presley concerts, in order to disperse crowds who were waiting for another encore. It’s since become a catchphrase and a punchline to refer to anyone or anything that has made a final exit.