Lovelorn Prince Lorenzo Borghese fended off flirtatious women who hunted the newly single Italian heir at the Last Chance Animal Rescue benefit in the Hamptons this past weekend. Borghese, founder of canine grooming brand Royal Treatment and best known for his role on “The Bachelor,” was noticeably sullen as he and his girlfriend of one year, Olga Turrey, had split on Friday. News of his eligibility must have traveled fast, a spy said, as “Women were all over him. It was comical.” Lorenzo said, “I wasn’t in the best mood because we had just broken up.”