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 about 7pm and attacked his wife with a tomahawk, then Amber when she got up.
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 Crown suggested his motive for the murders was to claim a life insurance payment so he could pay a debt.
The case was circumstantial and focused on a three-hour time frame and whether Lundy could have done what he was accused of doing and been back in Petone to call a friend at 8.30pm. The key witness for the police was Texas pathologist Rodney Miller, who gave damning evidence about two specks of tissue found on one of Lundy's polo shirts.
The appeal will challenge the credibility of the science used in the testing as "fundamentally flawed".
Mr Hislop grew up in Whangarei and was once a partner in Dallas Thorne and Partners. He works for London firm Doughty Street Chambers. He is a member of the human rights group Liberty. His firm said Mr Hislop's reputation was "a preparedness to defend the indefensible" and win.
Mr Hislop said he was "hopeful'' the Privy Council would find their arguments more attractive than the Crown.
"There is a certain exhilaration at putting your best foot forward.
"I think this is a very strange case. When you've been doing these cases for as long as I have, you don't get yourself bogged down with guilt or innocence.
"But one develops a feeling that something may have gone wrong in this case. When you think that someone is sitting in prison year after year and might even die there, it's a pretty chilling thought.''
He said he had a feeling that ``something wasn't right'' when he read the case file two years ago.
"We'll see whether their Lordships [the Privy Council] agree or not.''
The appeal before the five members of the Privy Council, including Chief Justice Dame Sian Elias, is likely to the last of its kind for New Zealand.
The decision on whether to quash Lundy's convictions will not be released for several weeks, if not months.
The Privy Council has reserved its decision on Lundy's appeal.