Lady Gaga, 31, who’s been filming Bradley Cooper’s “A Star Is Born,” was recently spotted house hunting out east with her boyfriend Christian Carino, a 48-year-old CAA agent. The adorable couple were seen at Gurney’s Residences, formerly known as Panoramic View, at 272 Old Montauk Highway in Montauk. That’s where they toured a $5.9 million, three-bedroom unit — twice, Gimme Shelter can exclusively reveal. “The singer loved Montauk so much that she is considering buying there,” our spy