Prince Lorenzo Borghese is sticking close to girlfriend Tinsley Mortimer as she grieves for her Chihuahua, Bella, who died Wednesday. Borghese attended the opening of the Empire Hotel rooftop Thursday hosted by Jet Set Events founder Peter James Cryan. But he left early to catch a morning flight to meet Mortimer at the Kentucky Derby. The socialite will head to the races after promoting her book “Southern Charm,” in Chicago. Proceeds from the Empire event went to Animal Aid USA.