Lockwood filed court documents on Thursday, ahead of the former couple's divorce and custody trial, set for Aug. 3. Lockwood and Presley, who split in 2016 after 10 years of marriage, share 11-year-old twin daughters, Harper and Finley.
In the filing, obtained by The Blast, Lockwood asks the court to strip Presley of primary custody, claiming "new and significant concern" over her potentially relapsing.
"Lisa Marie Presley's son shot and killed himself in her home (Although she was not there at the time.) With all due sympathy and respect, this creates a new and unaddressed twofold problem: the safety of the children and the greater likelihood of [Presley] to relapse into drug and alcohol dependency," the filing states.
A rep for Presley did not immediately respond to PEOPLE's request for comment.
Jeffrey Mayer/WireImage Lisa Marie Presley and Michael Lockwood
Last year, Presley opened up about her past addiction to painkillers and opioids in the foreword for Harry Nelson’s book The United States of Opioids: A Prescription for Liberating a Nation in Pain, revealing that she is "grateful to be alive today."
"You may read this and wonder how, after losing people close to me, I also fell prey to opioids," wrote Presley, who saw both her father Elvis Presley and ex-husband Michael Jackson die of complications from drug use.
"I was recovering after the  birth of my daughters, [Harper] Vivienne and Finley, when a doctor prescribed me opioids for pain," she added. "It only took a short-term prescription of opioids in the hospital for me to feel the need to keep taking them" due to their dangerous addictive properties.
Eric Charbonneau/Invision/AP/Shutterstock; Jon Kopaloff/FilmMagic Michael Lockwood, Lisa Marie Presley
Presley, who is also mother to 31-year-old actress Riley Keough, has attempted to keep her addiction private, however, details of her battle with sobriety emerged in the paperwork filed during her divorce from Lockwood.
In the book, Presley specifically mentioned her children as the purpose to stay sober. "As I write this, I think of my four children, who gave me the purpose to heal," she wrote after considering “the countless parents who have lost children to opioids and other drugs."
"[I'm] grateful to be alive today… and to have four beautiful children who have given me a sense of purpose that has carried me through dark times," she added
Lisa Marie Presley/Instagram Lisa Marie Presley and her children
Presley's 27-year-old son Benjamin, whom she shared with ex-husband Danny Keough, died on July 12.
Following Benjamin's death, a rep for Presley told PEOPLE that she is "completely heartbroken, inconsolable and beyond devastated," adding, "She adored that boy. He was the love of her life."
In the wake of Benjamin's death, Presley's rep said the star is "trying to stay strong for her 11-year-old twins and her oldest daughter Riley."
If you or someone you know is struggling with addiction, please contact the SAMHSA substance abuse helpline at 1-800-662-HELP.
If you or someone you know is considering suicide, please contact the National Suicide Prevention Lifeline at 1-800-273-TALK (8255), text "STRENGTH" to the Crisis Text Line at 741-741 or go to suicidepreventionlifeline.org.