Lockwood has not been charged with a crime and his attorney denies the claims made by Presley, 49.
"Mr. Lockwood and his lawyers believe that it is very unfortunate and inappropriate that Ms. Presley chose to file a one-sided, inaccurate version of the facts in the Family Law Court’s publicly accessible files," his attorney Jeff Sturman told ABC News in a statement. "Ms. Presley and her lawyers undoubtedly knew that their highly sensational, inaccurate and unproven claims would be of great interest to the media, which would disseminate Ms. Presley’s inaccurate story as a result."
The statement continued, "Mr. Lockwood is not going to publicly disclose very negative information about Ms. Presley to retaliate. Mr. Lockwood and his lawyers did not choose to litigate these personal matters in the press. Therefore, while Mr. Lockwood denies the truth of what Ms. Presley chose to put in the press, he has no further statement at this time."
Presley's rep and attorney declined to comment to ABC News.
Presley first contacted the Beverly Hills Police with allegations of child abuse in June 2016, the police department said in a statement to ABC News last week. Beverly Hills Police then contacted the Tennessee Bureau of Investigation after determining that the allegations stemmed from activity in Tennessee.
Beverly Hills Police did seize "several items" from a residence in the city, according to the statement, but said, "It is believed that there is no criminal activity related to these allegations in the city of Beverly Hills."
The department is continuing to work with Tennessee law enforcement to evaluate the evidence.
In its own statement, the Tennessee Bureau of Investigation said its agents work "to determine whether a crime occurred and whether it occurred in Tennessee. At this point, in this matter, we’ve yet to determine that to be the case."
The statement went on to add, "The work, however, to review potential evidence that might suggest otherwise continues. At this point, the TBI has not opened an official case in connection to this matter."
Meanwhile, the girls are living with their grandmother and Elvis Presley widow, Priscilla Presley, who posted pictures of them on Facebook.
"There is Lots of confusion, commotion and concern from all the talk circulating," she wrote in one post. "Let me put this to rest...the girls have not been in foster care and never will be. The girls have been with me and will be until all this is sorted out."
Later, the grandmother posted a second photo of the girls smiling and embracing.
"Thank you from the bottom of my heart for 'all' your positive support," she wrote.
Lisa Marie Presley and Lockwood, a guitarist and producer, married in Japan in 2006, but separated last June.
In the court documents, Lockwood is asking for $40,000 in monthly spousal support, but Presley says her $300 million fortune is nearly all gone and that she owes millions in back taxes and credit cards and has to pay for two full-time nannies for their children, when they visit with their father.