Nicola Edgington had also killed her mother six years earlier, but was released to live in the community.
She was found guilty at the Old Bailey last month of murdering Sally Hodkin, 58, and attempting to murder Kerry Clark, 22.
Both women were strangers and on their way to work in Bexleyheath, south-east London, in October 2011 when Edgington attacked them with a knife.
Shortly before, Edgington walked out of a mental health unit where she was taken by police after her mental health deteriorated.
John Cooper, QC, mitigating, said she was a woman in crisis and had not been given the help she asked for.
But the Recorder of London Judge Brian Barker said Edgington should stop blaming others for her actions and take responsibility.
He jailed her for life with a minimum term of 37 years for murder and gave her a concurrent sentence of life with a minimum term of 20 years for attempted murder.
Judge Barker told Edgington, 32, her behaviour had been “consistent and calculated”.
He said: “You are manipulative and exceptionally dangerous. What you did could not have been more selfish.
“I disagree that the responsibility for these acts can be laid on others.
“You made your choice and these were terrible acts for which you must take responsibility.
“You have come as near as can be to having three deaths on your hands.”
Miss Clark had escaped only with cuts to her hands because of her bravery and quick action, he said.
Edgington was said to have a borderline personality disorder and was found to be emotionally unstable and regularly blamed others for her situation.
She was ordered to be detained indefinitely at a secure hospital after stabbing her mother nine times in 2006.
Doctors diagnosed schizophrenia and she pleaded guilty to manslaughter on the grounds of diminished responsibility.
But medics at the Bracton Centre ruled she was well enough to be treated in the community after three years.
After two years of being monitored by a psychiatrist, nurse and social worker, her life began to unravel and her mental state deteriorated.
She was taken to the Queen Elizabeth Hospital in Woolwich by police after staff at a cab firm were alarmed at her behaviour in the middle of the night.
While waiting to be admitted, she rang 999 five times and warned that she was dangerous and would harm somebody if she was not sectioned.
After a delay, she was taken to the mental health unit, Oxleas House, but walked out soon afterwards and later complained that staff kept tapping on a computer.
The judge said: “It is unfortunate that the shift was changing and one of the doors was faulty.”
Edgington took a bus to Bexleyheath, bought a knife from Asda and attacked Miss Clark, who was waiting for a bus.
When Miss Clark grabbed the blade and kicked her away, Edgington ran to a butcher’s shop and grabbed a larger knife.
She attacked Mrs Hodkin, a law firm accounts clerk, with such force that she almost decapitated her.
Mrs Hodkin’s widower, Paul, told the court in a statement: “Forty years of marriage gone, wiped out in seconds by someone that should not have been on the streets.”
His solicitor, Daniel Rubinstein, said outside court: “While the family are relieved that a very dangerous woman has been taken off the streets, they remain concerned at the very many questions that remain over the actions of authorities and the alleged failure to treat clearly dangerous people in a secure environment.
“They will be considering further action to get answers in the hope that other families won’t have to go through the same appalling experience that they have.”
The sentencing came on the day that the Independent Police Complaints Commission found failings in the case.
It found that:
• Local police in Greenwich were not notified that Edgington was living in the area.
• Police and police staff did not carry out a police national computer check on Edgington which would have alerted them to her previous conviction for manslaughter.
• Officers missed an opportunity to use their powers under the Mental Health Act when Edgington tried to leave the A&E department shortly after she arrived with police.
• Edgington’s second 999 call from the A&E department was downgraded because she was considered to be in a place of safety and an officer was not asked to return despite Edgington saying she could be very dangerous. The police only contacted the hospital after a fourth call had been received.