Lundy is expected to be released on parole in May following a Parole Board decision this week.
He was convicted in 2002 of murdering his wife Christine and daughter Amber in their Palmerston North home in 2000. A retrial in 2015 arrived at the same judgement, re-imposing a life sentence with a minimum term of 20 years.
Forensic evidence showed the killings were particularly brutal.
Lundy, 66, has continuously maintained he did not kill his wife and daughter, and a group of supporters have formed around him to fight for his cause. In 2021, Lundy filed for his case to be reviewed by the Criminal Cases Review Commission.
Palmerston North residents want Lundy to stay away, the Manawatū city's mayor Grant Smith says.
"For the people of Palmerston North [the case] was quite confronting. I can recall at the time it really was almost disbelief that that had happened in our city.
"I think most people will be going: 'We don't want him in town, and I hope that he won't come back'."
At a Parole Board hearing on Thursday, Lundy said he would abide by the geographical restrictions placed on him when he is released.
Smith said he was surprised to hear Lundy had been granted parole, and hoped the release restrictions would stay in place.
"He wouldn't be welcome - regardless of what people think on all sides.
"And I'd have to say that those that were either connected to the trial or the police - even some family members, it's etched in their minds what happened with the murder of his wife and his daughter."
Lundy has served 23 years in prison and was denied parole in 2022 and 2023. His life sentence means that he can be recalled to jail at any time.
People living in the immediate area he will be residing will be notified of his whereabouts. He will be under a curfew and electronically monitored. The Parole Board has also met with the people he will be staying with.
Lundy is forbidden from using drugs or alcohol, which he can be tested for at any time, and is not allowed to use social media or dating sites, access pornography, talk to the media or contact any registered victims or their families.
Probation officers have permission to access any internet-capable devices he has.
Lundy told the Parole Board he has concerns about reactions to his release, including worries about his own safety and about any repeat of an earlier experience where media had arrived in the street he was staying in.
He had also previously met with hostility from some in the community - including being yelled at aggressively and told to drop dead. However, he told the board there had been more positive community interactions.
Lundy is scheduled to meet with the Parole Board in October to review his release.
