Acting since she was a child, Moss first came to wider attention as Zoey Bartlet, the teenage daughter of Martin Sheen's President Jed Bartlet, on Aaron Sorkin's series The West Wing before graduating - via the occasional movie role - to Mad Men.
Playing Peggy as the character has become more sensible and successful - last season she was poached by another agency - still presents a challenge, she says.
"It's a delicate balance between allowing her to grow and allowing her to change and retaining sight of the original Peggy that we love and not losing sight of the original person and the character that the audience has identified with.
"So it becomes easier in the sense that she becomes closer to myself, it becomes more fun because she is more confident and funnier, and you definitely want to have something new to play."
TotL certainly offers that. And not just because Peggy has rarely done a scene outdoors whereas Moss has been out in the wilds, scouring mountain ranges and lake edges most days during her months on the shoot.
"There's definitely pressure. It's the biggest thing I've ever done ... but I prefer to think of it as a challenge otherwise you'd get scared and I think that in the beginning you feel that more, but after two or three months you are just doing your job and trying to do the best job you can.
"The amount of stuff that you are involved in is pretty epic."
Moss had pursued the part after hearing about it. Campion had originally planned on using an Australian actress - partial funding by the Australian Broadcasting Corporation for the six-part series had depended on it - but didn't find anyone she thought was right.
"The material is quite difficult and quite complicated," says Campion. "You can't get away with just being real - you have to have some other quality that holds your interest. "And Lizzie did an audition that she sent to us and I guess we weren't holding out much hope. But for the first time we found ourselves riveted.
"She holds you and she's mysterious and I think for her it's a great role because it is so different from the Peggy character that she is so loved for in Mad Men.
"She's got that hardness but Lizzie stays open, she lets you in ... she can ground the work and she can keep it surprising."
Moss's Griffin, is a policewoman specialising in crimes against children, who, while visiting her ailing mother in Queenstown, gets involved in the life of young Tui Mitcham (Jacqueline Joe) when it's found the girl is pregnant. Griffin also has her own troubles to face including an old flame who has resurfaced. Moss: "It becomes a kind of diving down the rabbit hole kind of thing where she starts uncovering all the lies and secrets of this place and ends up going on this journey to look for this girl, but also look for herself."
Moss headed to the Queenstown-based shoot just a few days after wrapping the fifth season of Mad Men, arriving with the new Antipodean accent she had been practising for months.
"It's such a difficult accent," she says in her own Californian tones. "What we've done, and I think it's kind of important for us to stress, is that we are not trying to do a regionally specific Australian or Kiwi [accent] or whatever. We just wanted it not to sound American and we just wanted to tell the story. It's essentially Jane's accent.
"The whole thing from the beginning was 'let's not try to prove a point here, just take all the American out of it so that we can listen to the story'."
If Mad Men has one thing in common with TotL, is that's it's partly about sexual politics - though the Campion series is far more extreme.
"There's are things that are far worse than sexual harassment in the workplace going on. It deals with different elements of people's psyches and evil.
"It's a bit darker than the ass-grabbing that we've done on the show at times," she laughs "but both are equally important to show, I am sure."
Top Of The Lake starts on UKTV on March 25.
Mad Men's sixth season starts on SoHo on April 14.
- TimeOut
