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LITTLE ROCK, Ark. — Jack Greene's lawyers say he's severely mentally ill. The Arkansas death row inmate says they're lying.

As Greene approaches a Nov. 9 execution date, his lawyers are raising questions about who should determine his mental competency. Arkansas gives considerable weight to its prison director's opinion in deciding whether a condemned inmate has the mental capacity to understand his execution; Greene's lawyers want doctors to have a greater say.

"The system is really quite antiquated," John Williams, an attorney for Greene, said in an interview. "[Prison Director] Wendy Kelley is an arm of the state. She doesn't have the expertise to make that determination."

Greene was convicted for the 1991 killing Sidney Jethro Burnett after Burnett and his wife accused Greene of arson. At least one court this week will take up Greene's case.

This undated photo provided by the Arkansas Department of Corrections shows Jack Greene. Arkansas Attorney General Leslie Rutledge asked Gov. Asa Hutchinson to schedule an execution for Greene, who was convicted in the 1991 killing of Sidney Jethro Burnett after Burnett and his wife accused Greene of arson. Rutledge said Greene has exhausted his appeals and there's no stay of execution in place. AP

The inmate hasn't always made it easy for his attorneys. While pleading for clemency, he told the Arkansas Parole Board this month that his lawyers are wrong to call him "delusional" and that courts have routinely found him competent. He also told the board, "I knew what I was doing to him," when he tortured Burnett for an hour before shooting him. When a doctor testified that Greene has done headstands during examinations and even in courtrooms, Greene told the panel that he does yoga to remain "functional."

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Williams said the seemingly lucid moments mask severe mental illness.

Related: Arkansas Sets Execution Date for ‘Delusional’ Killer Jack Greene

"A lot of people who are mentally ill don't think they're mentally ill," the lawyer said.

The case has drawn the attention of both the American Bar Association and a collection of 28 mental health professionals, who wrote to Gov. Asa Hutchinson saying it would be "morally and ethically wrong" to execute Greene.

"Mr. Greene's illness manifests itself in extreme physical contortions, in self-mutilation, and in delusional beliefs he holds about a conspiracy against him between his attorneys and prison officials," the mental health professionals wrote.

Greene stood throughout his Oct. 4 appearance before the Parole Board, fidgeting and fumbling through documents that, he said, promised him a transfer to his home state North Carolina, where authorities said he killed a brother days before killing Burnett. Bloodied, rolled up strands of tissue stuck out of both ears and his left nostril; his lawyers said that is a symptom of Greene's mental illness.

"If I could go back to North Carolina and get medical treatment, that would be great, but if not, let's come on with this execution," he told the panel.

This undated photo provided by the Arkansas Department of Correction shows convicted murderer Jack Greene. Arkansas Gov. Asa Hutchinson's office announced on Friday, Aug. 25, 2017, a Nov. 9 execution date for Greene who was convicted of killing Sidney Jethro Burnett in 1991 after Burnett and his wife accused Greene of arson. AP

Williams says Greene believes he's being executed because he uncovered a purported (and to Greene, successful) conspiracy among guards and lawyers to torture the inmate and dissolve his central nervous system and spinal column.

"He thinks that the Department of Correction cannot send him back to North Carolina because he knows too much about what has happened to him in prison," Williams said. "They won't send him back to North Carolina, so they have to execute him."

Baloney, state lawyers say. North Carolina sent Greene to Arkansas for his murder trial on the condition that he would be returned if he received any sentence other than the death penalty. Greene knows a transfer is a lifeline, Assistant Attorney General Kathryn Henry said.

The governor said Friday that he was still reviewing Greene's file after Parole Board members recommended that he not spare the inmate's life.

Greene's execution would be Arkansas' first since it put four men to death in an eight-day period in April.