The 'Born To Die' singer is believed to have been in an on-off relationship with Barrie-James O'Neill, a member of the indie rock band Kassidy, for the past six months.
However, sources say that the couple are struggling to keep their relationship afloat as Del Rey's profile continues to rise.
"They make a very unlikely couple but they seem to work, and bounce really well off one another," an insider told The Mirror.
"Lana was due to appear on stage with the boys and sing 'Video Games' in December when they performed at Glasgow's Barrowland Ballroom. Unfortunately she was a no-show.
"She had a hectic promotional schedule, plus her management feared it would be a dead giveaway that she was seeing Barrie-James. They seem pretty smitten but because Lana's career has taken off so dramatically they're finding it increasingly hard to spend time together."
A spokesperson for Del Rey recently denied that a spring tour had been cancelled following the backlash over her Saturday Night Live performance, insisting that the 25-year-old had always planned to go on the road in October.
Watch Lana Del Rey in the video for 'Born To Die' below: