Sources connected to the Presley family tell us Michael Lockwood -- the father of 14-year-old twins Finley and Harper -- will absolutely go to court to get full custody of his daughters. As one source connected to Lockwood tells us, "It'll be a cold day in hell before he gives up custody of those children."

At the time of Lisa Marie's death, she had 60% custody of their twins ... he had 40%. Under California law, Lockwood would ordinarily get full custody, unless a judge determines he's not a fit parent.

Now here's the rub. Our sources say Danny Keough, Lisa Marie's ex who was living with her and the twins at the time of her death, sees himself as the stepfather of the kids. There's a ton of bad blood between Keough and Lockwood, and there are rumblings within the family he might fight to get custody of the kids.

Some members of the family have not discounted the possibility Riley Keough, the daughter of Lisa Marie and Danny, would also make a case for custody. And, there's talk Priscilla Presley might do the same. We do not know if either will actually make a move in court.

Now here's the wild card. The twins are old enough that the judge will give weight to their preference. We do not know their feelings about custody.

As you may know, Lisa Marie's divorce from Lockwood was incredibly nasty, with allegations of drug use and child abuse hurled around. It went on for 5 years.

TMZ broke the story -- Lisa Marie went into full cardiac arrest at home Thursday morning. Danny performed CPR until paramedics arrived, and while they were able to get a pulse, she died a few hours later at West Hills Hospital and Medical Center.

We're told Danny, Michael, the twins and other family members all gathered at Priscilla Presley's home Thursday night -- devastated by the loss.