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Pathologists suggested the material might contain cells found only in brain or spinal cord tissue but were unable to state that categorically, as the samples were poorly preserved.
The police then took the samples to Texas pathologist Dr Rodney Miller.
He was also unable to positively identify the tissue under a microscope but conducted an immunohistochemical (IHC) procedure, from which he categorically stated the tissue was from the brain or spinal cord.
The IHC procedure had never been used before in this manner.
At the original trial, the defence conceded the matter was brain tissue and the only issue was how it ended up on the shirt, possibly by accidental contamination during the police investigation.
But at the Privy Council hearing, Lundy's lawyer Dave Hislop, QC, submitted that the expert evidence given by Dr Miller, and others who relied on his opinion, was "fundamentally flawed" to the point that the trial was unfair. Three immunohistochemistry experts concluded the procedure was an "uncontrolled experiment" which was incapable of producing a reliable outcome.
Affidavits sworn by Professors Phillip Sheard, Helen Whitwell and Kevin Gatter concluded the tissue was poorly preserved and it was impossible to reach any conclusion as to the nature of the material.
They concluded the IHC procedure was an "uncontrolled experiment" which was incapable of producing a reliable outcome.
The Privy Council also heard evidence that IHC had been used sparingly worldwide to forensically identify tissue in criminal cases, with only one other example found.
On top of criticism of Dr Miller was the discovery of a previously undisclosed police document.
The report, written by the officer in charge of the murder case Detective Sergeant Ross Grantham, asked a senior officer for permission to visit Dr Miller in the United States.
He asked for the trip to be funded after neuropathologist Dr Heng Teoh said tissue was too degenerated to identify as brain tissue and Lundy should not be convicted on the strength of the cells on the slide he saw.
However, the document was not disclosed to Lundy's lawyers before the trial, denying them a line of inquiry for the defence.
Mr Hislop also attacked the science method which established the 7pm time of death evidence which was crucial to the prosecution case, calling a world expert who said analysing stomach contents was "so unreliable as to be of little value".
The theory that Lundy tampered with the family computer to create an alibi was also criticised by Mr Hislop, producing an affidavit from a forensic examiner saying a virus found on the computer could have caused the internal clock to be altered
Lundy is serving at least 20 years of a life sentence for the murders of his wife, Christine, and daughter, Amber.
The Crown case was that Lundy, then 41, went to Wellington on August 29, 2000, on a fortnightly sales trip to visit kitchen suppliers.
He checked into a Petone motel at 5pm, and 30 minutes later received a phone call from his wife telling him that Amber's Girl Guides meeting was cancelled and they were having McDonald's for dinner.
The Crown said Lundy convinced Christine to get Amber into bed by 7pm so they could have a romantic evening together.
He then drove 150km back to Palmerston North at high speed, parked 500m from his home, then ran inside around 7pm and attacked his wife with a tomahawk. When Amber got up to see what was happening, he killed her too.
Lundy then sped back to Wellington, arriving just before 8.30pm when he spoke to a friend on his cellphone.
Lundy's defence was that he stayed in Petone, read a book on the foreshore, drank alcohol and paid a prostitute to visit him at 11.30pm.
The bodies were found by Christine's brother around 9am the next morning.
Lundy was arrested six months later and was found guilty after a six-week trial in 2002.
How the case unfolded
August 29, 2000
Christine Lundy, 38, and daughter Amber, 7, are murdered in their Palmerston North home.
February 23, 2001
Mark Lundy is charged with two counts of murder.
March 20, 2002
Lundy is found guilty after a six-week trial.
April 12, 2002
Lundy is sentenced to life imprisonment with 17 years in jail before he can apply for parole.
August 12, 2002
Court of Appeal rejects Lundy's bid to have his convictions quashed and instead lifts his minimum non-parole period to 20 years.
November 29, 2012
Lundy files a petition asking the Privy Council for leave to appeal.
June 17, 2013
A three-day hearing in front of the Privy Council begins.
October 7, 2013
The Law Lords release their decision.
