The state of Virginia this week plans to carry out its first execution of a woman in nearly a century, despite claims that Teresa Lewis has severe learning difficulties.

Lewis's last hope is an appeal to the US supreme court after Robert McDonnell, the state governor, said he will not spare the life of the 41-year-old who was convicted of arranging for two men to murder her husband and stepson. She is scheduled to die by lethal injection on Thursday.

The men who carried out the killings – one of whom was Lewis's lover – received life sentences.

Lewis's last hope of avoiding the death chamber is an appeal before the supreme court. Her lawyers will argue that because she has such a low IQ her execution would be unconstitutional.

Prosecutors say that Lewis, a grandmother, deserves to be executed because she planned the killings in cold blood and bears a greater responsibility than the men who carried out the murders in order to collect insurance money.

Julian Lewis and his son Charles were shot in 2002 after an earlier attempt by Lewis to organise their deaths failed.

McDonnell, a strong advocate of the death penalty, said that an appeal for clemency before an execution is one of "the toughest decisions" a governor faces. He said he had read court transcripts and documents submitted by Lewis's lawyers but could see no reason why she should be spared. McDonnell said Lewis admitted to committing the "heinous crimes" for which she was convicted and dismissed claims by her lawyer that she is not mentally fit to be held responsible. The governor said that no medical professional has concluded that she is "mentally retarded" under Virginia law.

"The test for me really is: is there anything that would be a miscarriage of justice in letting the execution go forward?" he said.

Lewis's lover, Matthew Shallenberger, and another man, Rodney Fuller, shot the victims in their beds at a trailer home. Fuller confessed to the crime in order to save himself from the death penalty.

The judge in the case later said he could not impose a more severe sentence on Shallenberger for the same crime.

But he sent Lewis to the death chamber after describing her as the "head of this serpent".

Prosecutors portrayed her as scheming, saying she lured the two men into carrying out the murders with sex and the promise of a share of the insurance claim. Shallenberger has since killed himself.

The defence says that a psychologist tested Lewis and found she had an IQ of 72 which put her in the "borderline mental retardation" range.

The supreme court has ruled that the execution of "mentally retarded" people – interpreted by the courts as those with an IQ of less than 70 – is unconstitutional. Lewis has also been diagnosed with a dependency disorder and addiction to painkillers.

Defence lawyers also say Shallenberger told a former girlfriend that he "manipulated" Lewis in order to try and collect the insurance money on her husband so he could set himself up as a drug dealer in New York.

They say Shallenberger wrote to a friend from prison that "the only reason I had sex with [Teresa Lewis] was for the money – to get her to 'fall in love' with me so she would give me the insurance money".

However, prosecutors say that such claims are manufactured to save Lewis from the death chamber.

Among those who have appealed for her sentence to be commuted is the novelist John Grisham.

The last woman to be executed in the state was 17-year-old Virginia Christian in 1912 for the murder of her employer after she was accused of stealing a gold locket.

There are 53 women on death row in the US. They include Linda Carty, who is from the Caribbean island of St Kitts and who holds a British passport but spent most of her adult life in the US. Carty was convicted, along with three co-defendants, of murder in Texas after kidnapping a 25-year-old woman and her three-day-old baby.

The woman was tied up with duct tape and a bag sealed over her head before she was forced in to the boot of a car where she died of suffocation.

Carty's co-defendants testified against her and were spared the death penalty. She says she was framed by them because she was an informant for the Drug Enforcement Administration. Carty is facing execution after the US supreme court refused to hear an appeal.

The ultimate penalty

Eleven women have been executed in the US since the restoration of the death penalty in 1976. The first was Velma Barfield. She was put to death in North Carolina in 1984 for putting rat poison in her boyfriend's tea after fearing he had discovered that she was forging cheques on his bank account.

Karla Faye Tucker drew international attention before her execution in Texas in 1998 because she became a born-again Christian while in prison and pleaded with the state's then governor, George Bush, for clemency. Tucker was convicted of murdering two people with a pickaxe during a robbery with two men. Bush refused to commute her sentence.

Christina Riggs, a nurse, was put to death in Arkansas in 2000 for smothering her two small children. After killing them, she wrote a suicide note and took an overdose of pills, but survived. During her trial she would not let her lawyers argue against the death penalty, saying she wanted to die. When the jury obliged she said "Thank you".

Lois Nadean Smith was executed in Oklahoma in 2001 at the age of 61 for killing her son's former girlfriend. Smith shot Cindy Baillie nine times after accusing her of plotting to have her son killed. Smith's lawyers told the court she was trying to protect her son and was under the influence of drink and drugs at the time of the killing.

Aileen Wuornos was unusual as a female serial killer who received six death sentences and was executed in Florida in 2002. Wuornos, a prostitute, admitted murdering seven men. She claimed they had raped her or attempted to. She was the subject of the 2003 film, Monster.

The most recent execution of a woman was in 2005. Frances Newton was put to death in Texas for the murder of her husband and two children, aged seven and one. Prosecutors said she did it to claim $100,000 (£64,000) in life insurance. Newton claimed her husband was a drug dealer who was murdered because he was in debt to suppliers.