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Lundy is serving 20 years in prison for murdering Christine Lundy and seven-year-old 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.
A spokesman for Mark Lundy support group Factual (For Amber and Christine - Truth Uncovered about Lundys) said a new appeal was lodged with the the judicial committee of the Privy Council in London yesterday.
Mr Lundy would be represented by lawyer David Hislop QC, a New Zealander who now works in the UK.
Factual was largely funding the appeal, the spokesman said.
"Most of it's pro bono really. We've had a lot of people work pro bono and all of the scientists worked free of charge."
Should it go ahead, the appeal could be one of the last of its kind - the Supreme Court replaced the Privy Council as New Zealand's highest court in 2004.
According to the Supreme Court Act, 2003, the Privy Council can still determine appeals in certain existing proceedings, including appeals against Court of Appeal judgements made before January 1, 2004.