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Barrie-James O'Neill is either a man deeply in love and willing to fight for his woman ... or deeply delusional ... because he says he and Lana Del Rey have NOT broken up.

Del Rey told a German outlet earlier this week the two were no longer together ... saying, "He is a wonderful person, but there are some things with which he has to deal ... I no longer felt free."

So our photog tried to get the truth out of the rocker at LAX on Tuesday night and he scoffed at the reports -- even though it came straight from Lana -- telling us not to believe everything we read.