McGuire struggled, made guttural noises, gasped for air and choked for about 10 minutes before he was declared dead, after prison officials used the new two-drug execution method at the Southern Ohio Correctional Facility in Lucasville, the Columbus Dispatch reported.
Allen Bohnert, one of McGuire's federal public defenders, said the execution Thursday was a "failed, agonizing experiment by the state of Ohio."
"The people of the state of Ohio should be appalled by what was done in their name," Bohnert told reporters.
McGuire was convicted of aggravated murder for the 1989 rape and killing of 22-year-old Joy Stewart.
"There has been a lot of controversy regarding the drugs that are to be used in his execution, concern that he might feel terror, that he might suffer," Stewart's family said in a statement. "As I recall the events preceding her death, forcing her from the car, attempting to rape her vaginally, sodomizing her, choking her, stabbing her, I know she suffered terror and pain. He is being treated far more humanely than he treated her."
Bohnert refused to speculate whether McGuire suffered, the Dispatch said.
The lawsuit, to be filed in federal court, will allege the state violated the U.S. Constitution's ban on "cruel and unusual punishment."
McGuire received an injection of the sedative midazolam and the painkiller hydromorphone. Ohio switched to the two drugs for intravenous injection for McGuire's execution because the drug used in the past is no longer available, as European manufacturers won't sell it for use in U.S. executions.