However, she refused to be drawn into more detail about the case, specifically in relation to the reliability of evidence used at Lundy's first trial in 2002.
"I can't really comment on individual cases, particularly a matter which is now before the courts again, so it's difficult to do that," she told TVNZ political editor Corin Dann.
"But that's a matter which will no doubt be canvassed during the retrial."
Earlier this week the Privy Council overturned Mr Lundy's convictions for the murder of his wife Christine and daughter Amber, 7, in Palmerston North in 2000.
The Law Lords unanimously voted in favour of the appeal, and said the case should be tried again amid concerns about the reliability of scientific evidence and police disclosure in the case.
Ms Collins was adamant the justice system "is working" following criticism over high-profile cases, such as Lundy's and David Bain's which have poured doubt over police methods and reliability of evidence.
"The public shouldn't have any loss of confidence,'' she said.
However, she conceded that "sometimes police will get things wrong", but added: "The vast majority of the time, they don't.
"We have 85,000 criminal convictions a year in this country. Of those, only 1 per cent are appealed, and of that 1 per cent that are appealed, only 10 per cent are successfully appealed. So that's about 99.9 per cent of all criminal convictions every year are upheld."
Ms Collins continued: "[H]alf of all people convicted of murder in this country will appeal. And I don't believe for a moment that half of all the people convicted of murder are not guilty, but half of them will appeal."
She denied prisoners face difficulty appealing their convictions, and said there was no need for a change in the current system to one more like the UK.
"[T]he fact is that when you have such a tiny minority of people appealing under the current system, that tells me that a lot of people accept their convictions," Ms Collins said.
