Lana Del Rey has a message for Barrie-James O'Neill ... check out this photo and then get a clue ... WE'VE BROKEN UP! Lana was in Portofino, Italy, sucking face with Francesco Carrozzini who has directed a bunch of music videos with famous singers like Beyonce and Rita Ora. Our photog shot O'Neill a week ago at LAX and he told us reports he broke up with his girlfriend of 3 years were B.S. If O'Neill is right ... Lana is one convincing -- and hot -- liar.