"We are all reeling from the sudden passing of Lisa Marie Presley, the mother of my two beautiful twin daughters Harper and Finley," the musician said in a Wednesday, January 18, statement. "Nothing prepares us for such an unexpected tragedy. It is incomprehensible."
"The most important thing to me at this time is to take care of my daughters, making sure they always feel safe and loved," he continued. "Both of them have incredible spirit and they will carry our family's legacy on for the rest of their lives."
"Since they were born, Harper and Finley have brought me profound joy and I remain devoted to them," he added. "We ask for privacy at this incredibly difficult time."
As OK! previously reported, Presley was rushed to the hospital on Thursday, January 12, after being found unresponsive in her Southern California home by a housekeeper. Her ex-husband, Danny Keough, who happened to be at her house at the time, performed CPR on her until medical personnel arrived.
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Doctors placed her on life support shortly after she arrived, and later that night, she suffered a second cardiac arrest leading to her death.
"It is with a heavy heart that I must share the devastating news that my beautiful daughter Lisa Marie has left us," her mother, Priscilla, wrote in a statement at the time. "She was the most passionate, strong, and loving woman I have ever known. We ask for privacy as we try to deal with this profound loss. Thank you for your love and prayers."
Prior to her passing, Lockwood and Presley had previously been locked in a heated custody battle following their 2016 split. She was eventually ordered by the court to pay over $6,000 per month in child support to support their two daughters.
It is unclear if the guitarist plans to go after the Presley estate to continue the child support payments.
People reported Lockwood's statement.