Instead, he was interviewed by Cohen in character as Colonel Erran Morad, who waved a "paedophile detector" at him.
During his campaign for Senate, Moore was accused by multiple women of sexual misconduct, including one allegation that he sexually assaulted a 14-year-old girl when he was in his 30s in 1979.
The lawsuit claims Moore was invited to Washington, D.C., "to receive an award for his strong support for Israel in commemoration of its 70th anniversary as a nation state".
The lawsuit ultimately claims the "fraudulent portrayal and mocking of Judge Moore as a sex offender" on the television show "severely harmed" his reputation and caused his family "severe emotional distress", as well as "financial damage".
This combination photo shows Sacha Baron Cohen, left, at the Vanity Fair Oscar Party in Beverly Hills, Calif. on March 4, 2018, and former Alabama Chief Justice and U.S. Senate candidate Roy Moore at a news conference in Birmingham, Ala., on November 16, 2017.
Roy Moore in a still from 'Who Is America?'
First Nike Kaepernick ad to air during National Football League opener
Nike will feature Kaepernick on several platforms, including billboards, television commercials and online ads. And now, the first video ad featuring Colin Kaepernick just rolled out.
Representatives for the Moore family did not respond immediately to a request for comment.
"I've been married for 33 (years)", Moore replies.
Showtime issued the following statement: "The press has been sent copies of an alleged complaint, yet to our knowledge SHOWTIME has not been served".
The filing demands a jury trial and seeks damages in excess of $95 million "and any other relief that this court may deem just".
A release form signed by Moore for his appearance on the program, the complaint continues, was invalid due to the supposedly fraudulent conditions under which it was signed.
According to the lawsuit, Cohen, "while in character, falsely and fraudulently induces unsuspecting victims, such as Judge Moore to be interviewed under dishonest, unethical, illegal and false pretenses".
"Had Judge Moore and Mrs. Moore known that "Erran Morad" was Defendant Cohen, Judge Moore would have never agreed to be interviewed", Moore's lawyer wrote in the lawsuit.