Brad Raffensperger, Georgia’s Republican secretary of state, has been forced to spend half a million dollars defending himself in court for having stood up to former President Donald J. Trump’s efforts to overturn the 2020 election.

The only way to spare himself from the defamation lawsuit he has been fighting, he and his lawyer say, would be to lie.

The lawsuit centers on a 2020 video that purported to show election fraud in Georgia. The video, which was presented to state lawmakers, showed security footage of election workers tabulating ballots in Atlanta. Multiple news media outlets and the secretary of state’s office have debunked the claims of election fraud made in the video presentation to legislators.

The plaintiff in the case, Jacki Pick, a Texas-based Republican podcast host who guided the lawmakers through the 30-minute presentation, sued Mr. Raffensperger for defamation over how he described the video in his book, “Integrity Counts.” He wrote that the video “had been deceptively sliced and edited.” Ms. Pick, who is married to the Texas multimillionaire and megadonor Doug Deason, claims she was defamed, even though Mr. Raffensperger’s book never mentioned her by name.

Ms. Pick’s lawyers let it be known that if Mr. Raffensperger wanted to settle the case, he would first have to say publicly that her presentation of the video was not deceptive. In other words, Mr. Raffensperger says, he would effectively have to tell his own new lie.