Lundy will not appear at the hearing.
Police have visited the Taupo house to check on its suitability. Mr Jones did not want publicly reveal his address in Taupo.
"It's a chicken and egg situation really isn't it ... it's got to be approved yet, and we need to wait until that happens.
"I expect we will get a lot of rubberneckers coming past but I'm hoping it won't last long."
Mr Jones and his wife Caryl - Lundy's sister - had been in regular contact with him since he was convicted of the double murder of his wife, Christine, and daughter, Amber, in August 2000.
"We've always seen him as often as we could ... it's become more regular since he was transferred to Rangipo."
The couple attended the three-day Privy Council appeal hearing held in London in June.
The Privy Council released a reserved decision on Monday to allow the appeal, quash the murder convictions and hold a re-trial.
The Jones' visited Lundy at Rangipo Prison, where they have visited him regularly on Sundays, immediately after the decision was reached.
Lundy would also call them on the phone two or three times a week from the prison.
Lundy was "ecstatic" when the couple saw him on Monday.
"He was very happy ... quite relaxed, it's a huge weight off his shoulders.
"Finally the facts have been listened to after all these years."
Mr Jones said having Chief Justice Sian Elias on the five-member Law Lords panel of the Privy Council had been crucial.
"She is a New Zealander and she listened to the facts.
"The appeal decision was unanimous, five to zero.
"From the day he was arrested ... now finally someone has listened.
"There's been a lot of emotion involved in all of this but nothing stacked up."
Mr Jones had "no idea" who may have committed the murders.
"I honestly don't think the police adequately investigated all of the case ... they stuck to the 7-7.30pm time frame."
Police now had a "huge task" ahead to re-investigate the murder, he said.
"There were around 60 suspects who had alibis which police will have to go back and recheck."
