The Boston headquarters of the television show “Gilded Lilys’’ was bustling yesterday afternoon. That’s because the ABC pilot, which will be filmed around the state this month, starts its shoot today. “Lilys,’’ which is follows the opening of the first luxury hotel in New York City 1895, is being helmed by “Grey’s Anatomy’’ showrunner Shonda Rhimes with her frequent collaborator, Milton Academy grad Betsy Beers. . .