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A spokesman for the Privy Council this morning said Lundy's application to appeal had been accepted and a three-day hearing would take place in London during the week starting June 17.
Lundy is serving 20 years in prison for murdering his wife Christine and 7-year-old daughter Amber in a brutal axe attack in their Palmerston North home in August 2000.
In 2002 he lost an appeal to the Court of Appeal and had his non-parole period increased to 20 years, the longest non-parole period of imprisonment for a life sentence ever handed down in New Zealand.
Lundy's London-based lawyer, David Hislop QC, said the appeal would pivot on the science used to identify brain tissue found on a shirt.
"We say [it was] flawed science, bad science, and we obviously want to argue that," Mr Hislop told RadioLIVE this morning.
"It was never good science. In essence, what was deployed from the scientists from Texas was a scientific experiment. He'd never done it before, the science world had never done it before and we say he's got it wrong."
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Mr Hislop said the argument about whether Lundy had time to commit the murders by driving from Wellington to Palmerston North and back in two hours and 58 minutes in peak hour traffic had "very little to do" with the appeal.
Mr Hislop said he was "delighted" at the Privy Council's decision and he had not yet spoken with Lundy or lawyers in New Zealand.
"We're delighted. We've put a lot of hard work into this, and we want to see that Mark gets the very best opportunity that he can to put his story across," he told RadioLIVE.
Mr Hislop said the defence team would need to raise money to fly New Zealand scientists to London to give evidence as part of the Privy Council appeal.
Lundy's defence relied on evidence from those scientists, he said.
If the appeal was successful, the case would likely be sent back to New Zealand for a retrial, Mr Hislop said.
The Privy Council spokesman said the right to appeal was granted by three justices of the court who decided on submissions by Lundy and the Crown whether there was merit for an appeal to take place.
"Given the high profile of this case, we will also seek to make arrangements to live stream the hearing from London over the internet," the spokesman said.
- Kieran Campbell