Nathan Vaughan-Jones, 34, had been jailed for 11 years in March after pleading guilty to the manslaughter of 63-year-old Nigel Ross on the grounds of diminished responsibility.
On July 1, sex offender Colin Morton was also found dead at the prison. The Ministry of Justice has not yet confirmed how he died or whether he was being treated as a suicide risk at the time.
The death of Foster, a former Detective Constable, will now be investigated by the independent Prisons and Probation Ombudsman, along with all deaths in custody.
A spokeswoman for the Prison Service said: "HMP Lewes prisoner Peter Foster was found hanging in a cell at 3am on Monday July 30.
"Prison staff tried to resuscitate him and paramedics were called but he was pronounced dead at 3.25am.
"As with all deaths in custody, the independent Prisons and Probation Ombudsman will conduct an investigation."
During the court hearing, Philippa McAtasney QC, defending, said Foster had made a "serious" attempt to commit suicide while on remand and was staying on a mental health wing of the prison.
The court heard Foster killed Heather Cooper in front of their two young children, Joshua, now three, and Isabel, who was three months old at the time.
Benjamin Aina QC, prosecuting, told the court Foster took time to clean up the blood-soaked crime scene and took Miss Cooper's body to the woodland, where he covered it with bracken.
He told his cousin, David Foster, some of the details about what happened, leading him to alert the police. Foster led officers to where he had hidden Miss Cooper's body, telling them they should arrest him for murder.
He then claimed he acted in self defence as Miss Cooper attacked him, later turning to aggression.
Sentencing Foster, Judge Richard Brown described him as an "extremely dangerous individual" who may never be safe to be let out of prison.
He said: "This was a wicked, savage and senseless attack on a young mother in her own home.
"Not only have you taken her life, you have also deprived Joshua and Isabel of a loving mother and, no doubt, devastated her family and friends."
The judge added that aggravating factors were that the attack was carried out in front of the couple's children, that the defendant was trained in martial arts, and the ferocity of the attack, which involved two weapons.
He told him: "Whether or not you will ever be released will be a matter for them.
"Many matters may point to you being an extremely dangerous individual.
"However, that's a matter for the Parole Board, not me."
Miss Cooper, who grew up in York, joined Surrey Police in 2003 and worked in the Public Protection Investigation Unit based at Guildford police station.
During her career she received several letters of praise from senior officers for her work on various crimes and in 2009 was given a commendation by the force for her "professionalism, dedication and commitment".
In a victim impact statement read to the court, Miss Cooper's parents, James and Caroline Cooper, said the murder had an unimaginable impact on the two children who witnessed it.
"Through her death, Heather lost her children for 50 years of her life, Joshua and Isabel have been given a life sentence by the loss of their devoted mother.
"Heather would have been devastated to know she would not be able to bring up her children and Isabel would never know her mummy and Joshua would suffer grief at such a young age."
Lewes Prison in Lewes, East Sussex is a 742-capacity Category B men's prison.
