A jury found him guilty on two counts of murder.
In 2007, he was jailed for at least 21 years - one of New Zealand's longest minimum-term sentences.
But the next month, Gunn's family learned Reihana was set to undergo a $1 million bone marrow transplant after being diagnosed with leukaemia.
The Department of Corrections said it had a "statutory olbigation" to ensure prisoners receive "the same standard of care that they would expect in the community".
"A prisoner's level of care, including room type, is determined by the relevant DHB and the assessment of the medical team. Health service providers working with a prisoner are provided with appropriate knowledge of the patient's background," Corrections said in a statement.
"As we also have a duty of care towards the prisoner to protect their privacy and security, we do not advise other patients of an offenders' identity."