The case could test whether the firing squad is constitutional, said Kent Hart with the Utah Association of Criminal Defense Lawyers.
"It's a gruesome death," Hart said Tuesday.
Utah is the only state that allows executions by firing squad if lethal injection drugs aren't available. Utah lawmakers said the approval was a practical matter of choosing a backup plan to the drugs that have come under increasing scrutiny.
Opponents, however, say firing squads are barbaric.
Lafferty is the longest-serving death row inmate in Utah and one of the inmates who is closest to a possible execution date. He was convicted in the 1984 deaths of his sister-in-law, Brenda Lafferty, and her baby daughter. He claimed the killings were directed by God because of the woman's resistance to his beliefs in polygamy.
His opposition to a firing squad was voiced Friday in a federal court motion asking a judge to put his case on hold so he could pursue complaints about evidence handling and testimony. His lawyers also argued that lethal injection is unconstitutional.
No deadline was set for U.S. District Judge Dee Benson to rule on the motion. The state currently has no lethal injection drugs on hand.
The argument that the death penalty is unconstitutional is common in death penalty appeals, said Utah lawyer Greg Skordas.
"Those motions are filed in every death penalty case in Utah that I've ever seen," he said.
But in the Lafferty case, attorneys could call experts to testify about suffering during firing squad executions.
Tom Brunker, the state attorney who oversees capital cases, has said he expects the constitutionality of the method to be tested the first time it comes up, though that's likely years away.
Under the Utah law signed in March, inmates would be executed by firing squad if the state is unable to get lethal injection drugs a month in advance.
Utah lawmakers had stopped offering inmates the choice of firing squad in 2004, saying the method attracted intense media interest and took away attention from victims.
Utah is the only state in the past 40 years to carry out such a death sentence, with three executions by firing squad since the U.S. Supreme Court reinstated the death penalty in 1976.
The last was in 2010, when Ronnie Lee Gardner was put to death by five police officers with .30-caliber rifles. Gardner killed a bartender and later shot a lawyer to death and wounded a bailiff during a 1985 courthouse escape attempt.
The Associated Press