(CNN) Six of the eight men Arkansas planned to execute over an 11-day period this month are not mentally fit for the death penalty, a report by a Harvard Law School initiative suggests.

The report by the school's Fair Punishment Project says that between mental illnesses, intellectual disabilities and "bad lawyering," the orders for all eight of the executions may never have been justified.

"Nobody is questioning whether people who commit some of the most serious offenses should be held accountable," said Rob Smith, executive director of the project, which seeks to create a fair and accountable justice system.

"The question is, do people who are among the most broken, vulnerable and impaired in our society deserve the death penalty," he said, as opposed to life without parole.

A flurry of last-minute court rulings and appeals raised doubts whether Arkansas would be able to execute any of the men this month as planned. But late Thursday night, the first of the eight, Ledell Lee , was put to the death.

Of the inmates originally scheduled to die, one has been diagnosed with bipolar disorder, another has suffered with hallucinations, two have IQ levels indicative of intellectual impairment, and most have experienced severe abuse, according to the Fair Punishment Project's report.

Each has been convicted of murder, and most have been on death row for a couple of decades.

The lethal injections were set to begin April 17 and continue through April 27 in a rash of executions unlike anything seen since states reinstituted the death penalty in 1976, according to the Death Penalty Information Center

hadn't put someone to death since 2005, so why Until Thursday night, Arkansashadn't put someone to death since 2005, so why the sudden rush

The state's supply of midazolam, a controversial drug meant to sedate inmates during lethal injections, will expire at the end of April. And Gov. Asa Hutchinson said in an earlier statement to CNN it is his "duty" to "carry out these lawful sentences imposed by juries and upheld by the Arkansas Supreme Court" before it's too late.

The Eighth Amendment "bans cruel and unusual punishment," said Jeffrey Toobin, CNN's senior legal analyst. "Part of the issue of who can be executed is whether they can understand why they're being executed. ... If you don't understand why you're being punished, the death penalty doesn't serve the purpose it's supposed to serve."

While "the vast majority of those on death row are poor and ignorant and mentally damaged in one way or another," Toobin said, "the general rule is mental illness does not get you out of being executed; only mental retardation does. But the lines around those conditions are not extremely clear."

In its report, the Fair Punishment Project outlined the histories of each of the eight men who had been scheduled to die this month. The report was based on court pleadings and opinions, transcripts of expert testimonies, and witness affidavits. Here's a summary of the report's findings

Don Davis

Don Davis was supposed to be put to death April 17 and had been served his last meal was supposed to be put to death April 17 and had been served his last meal before the US Supreme Court refused to overrule a state court ruling -- thereby delaying his execution . On two IQ tests he took as a child, Davis scored a 69 and a 77, signaling intellectual impairment, court documents show. He also suffered a serious head injury and, coupled with his low IQ level and attention-deficit hyperactivity disorder, experiences " 'double deficits' in cognitive functioning," the report states. Soon after his birth, both his parents abandoned him. Davis "never received a comprehensive mental health evaluation by an independent expert," the report found. He has spent more than 25 years on death row.

Jack Jones

• Serious mental illnesses have plagued Jack Jones since childhood, the project's review of documents showed. He endured paralyzing hallucinations and, at times, would be found rocking and banging his head against cupboards. He was abused by his father and abducted and raped by three strangers. He attempted suicide twice before he finally got psychiatric attention. He committed himself to a hospital for severe depression and suicidal ideation just months before he committed murder -- and was diagnosed with bipolar disorder not long before his crime. The jury heard "almost none of this," the report states. Jones was scheduled to die April 24.

Marcel Williams

• Marcel Williams' first experience with sexual abuse was when his mother offered him up to a friend when he was just 9 or 10, legal documents show. Starting at 12, his "'mother was routinely pimping him ... in exchange for food stamps, for food, for a place to stay'" to women 10, 20, 30-plus years older than him, the report quotes. He was gang-raped while in an adult prison where he served time as an adolescent. He was beaten severely and regularly by his mother, who once burned him with an electric coil. He was raised in abject poverty and didn't always have shoes. A judge reversed his death sentence because Williams' history wasn't presented to a jury, but an appellate court reinstated the sentence. Williams also was set to die April 24.

Kenneth Williams

• Kenneth Williams has an IQ of 70, a history of "neuropsychological problems" and "severe learning disabilities," testimonies showed. He bounced between six foster homes and often wasn't adequately fed. His own parents abused drugs, and he endured physical abuse. Evidence suggests that he's suffered brain damage, having exhibited a tremor, deficient motor skills and problems with memory. He has trouble focusing or comprehending what he reads or hears and has shown deficiencies when it comes to reasoning and judgment. He began smoking marijuana at 6 and turned to beer by 9 -- the same age he was when he was first institutionalized in the juvenile system. He was set to die April 27.

Ledell Lee

Stacey Johnson

• The review of records for Ledell Lee and Stacey Johnson show inadequate legal representation, the report found. In the case of Johnson, whose conviction was based in part on the inconsistent testimony of a 6-year-old girl, there remain questions about his guilt, the report said. And no evidence exists that Johnson's lawyers ever looked at his life history.

On Wednesday, the Arkansas Supreme Court issued a stay of Johnson's execution, allowing for further DNA testing that might prove his innocence. He had been scheduled to die Thursday.

A claim that Lee was intellectually disabled was introduced at one point, the report showed, but the federal defender who introduced that was removed from the case.

A brief filed Wednesday on Lee's behalf by a new legal team argued for clemency and requested DNA testing. The brief stated that Lee had "serious neuropsychological deficits stemming from Fetal Alcohol Syndrome Disorder," showed "evidence of possible brain damage resulting from a boxing injury as a child" and likely had "either borderline or mild intellectual disability."

Jason McGehee

Jason McGehee was scheduled to be executed April 27 but was was scheduled to be executed April 27 but was granted a temporary stay of execution April 6. McGehee's mental fitness wasn't a factor; instead, a clemency recommendation by the parole board based on good behavior prompted the stay.

But the Fair Punishment Project's report found that McGehee has bipolar disorder, which went untreated when he was a child, and has shown evidence of brain damage and frontal lobe impairments. He was abused by his father, his mother and later his stepfather -- who kicked McGehee's dog to death while forcing McGehee to watch. "Jason was never the same after that," his aunt said in a court petition, though none of this was presented during his trial.

Bruce Ward

• On April 14, the Arkansas Supreme Court granted a stay of execution for Bruce Ward, who had been scheduled to die April 17.

According to the Fair Punishment Project report, he didn't understand what was coming. He believed he was about to set off on a "special mission as an evangelist," according to a complaint cited in the report. He told a forensic psychiatrist in 2010 he hears voices, he gets revelations directly from God and he will "walk out of prison to great riches and public acclaim." He said he's been visited in prison by his deceased father and "resurrected dogs." It's believed that mental illness runs in Ward's family.

He was 4 when his mother had a mental breakdown. She beat him regularly, put tar on him before submerging him in ice-cold water and forced him as a young boy to sleep naked beneath water that dripped through a leaking roof.

"We are grateful that the Arkansas Supreme Court has issued a stay of execution for Bruce Ward so that they may consider the serious questions presented about his sanity," Ward's attorney, Scott Braden, said in a statement last week. "His nearly three decades in solitary confinement have only worsened his severe mental illness."