The freelance cameraman who taped the conversation and gave it to the Herald on Sunday says it was recorded by accident.
Mr Key says he does not believe this and has complained to the police. No one has published the conversation.
Mr Lewis said he believed it was in the public interest for the transcript of the tape to be released.
"There is a difference between the News of the World hacking into someone's phone to find out private information and seemingly - whether accidentally or on purpose - effectively a journalist investigating some kind of political statement.
"But if it's particularly a political statement which affects the future government or the ways to achieve future government in a country, then that's something in the public interest and it sounds like it should be reported without the unfavourable comparison to what was clearly a criminal act."
A spokeswoman for Mr Key said he stood by his statements and that "there is no place in this country for News of the World-type secret taping tactics, targeting any New Zealander".
Milly Dowler, 13, was abducted on her way home from school in Walton-on-Thames, Surrey, on March 21, 2002, and subsequently murdered.
Her remains were found months later, and former nightclub bouncer Levi Bellfield was found guilty in June this year of her murder.
This year it was revealed that the News of the World hacked into Milly's phone at a time when her family hoped she might still be alive.
The newspaper deleted messages on her phone to free space, giving the family false hope that Milly was alive.
News Corp boss Rupert Murdoch closed the 168-year-old paper in July because of the public outrage and flew to Britain to apologise to the Dowler family in person.
It has been reported that News Corp is trying to negotiate a settlement with the Dowlers and has offered them £2 million (NZ$3.9 million).
Mr Lewis said there was a difference between taping the PM speaking about something which could be deemed "very crucial politically" and recording him talking about personal matters, like his health or his family.
"If it's to do with how the country is governed then that's good journalism," he told 3 News. "The public choose their politicians ... they really ought to know wherever they are in the world."
Mr Lewis was himself a target of the News of the World after he represented another hacking victim.
The real comparison, he said, was to former British Prime Minister Gordon Brown's gaffe when a microphone he was wearing picked up his comments that Labour supporter Gillian Duffy was a "bigoted woman".
"Politicians need to be careful about TV cameras and microphones. They should watch out that things aren't recording."
Earlier yesterday, Mr Key said his police complaint was based on principle.
"What happens when it moves to other high profile New Zealanders having a conversation with their wives about personal issues?
"What happens if a couple of high profile New Zealanders have a conversation about their son or their daughter being suicidal - a Sunday paper reports that and that child takes their own life. We're at the start of a slippery slope here and I for one am going to stand up and ask the police to investigate it."