A source told the US publication: "They were thrown together at a dark point and found they have much more in common than anyone realised."
"They were put in touch by a mutual friend. The attraction is wild.
"They're in love and have a lot in common," the insider added.
According to the Globe's report, the two have bonded over their growing legal troubles.
Lisa Marie is suing Barry Siegel, contending he lost the $100 million trust left to her by her father, Elvis Presley.
Meanwhile, Johnny's suing his former business managers, who claim his shrinking movie fortune is due to out-of-control spending.
Another source told the publication, "Johnny and Lisa Marie are working through their troubles together."
"They're giving each other advice and bonding over their love of music."
Neither Johnny or Lisa Marie have responded to the Globe's report.