He died on Monday after an incident at Kohuora, the Auckland South Corrections Facility in Wiri.
A spokesperson for Serco, which runs the facility, said a paiāki (men in our care) in a self-care residence contacted staff concerned about another person in distress.
"Staff arrived at the residence two minutes after the initial call. An ambulance was called and the man was taken to hospital.
"Police were also called to Kohuora while the paramedics attended to the paiāki.
"Later this morning we were advised by the hospital that the paiāki had died. There is no indication that the death was suspicious."
The site had been secured to preserve the scene and the Inspector of Corrections had been advised.
"We are providing additional support to his housemates."
The death would be investigated by the Coroner.
The murders happened on April 13, 2003, when Lin had come to pick up her things from Cui's Unsworth Heights home on Auckland's North Shore.
A jury was told Cui had repeatedly stabbed Lin and cut her throat in his bedroom.
He then went outside and stabbed two men, who were waiting in a car for Lin, before he fled the scene.
He was eventually arrested in Paihia.
