It’s very late on Sunday night in New York and Cyndi Lauper is contemplating the busy Monday ahead. She has to take her 10-year-old son Declyn to school, work out with her fitness trainer, and get the studio equipment ready for the visiting Swedish songwriters and co-producers to record one last vocal.

She hopes the rhythm and hip-hop-influenced album – which may be called Life, or Savoir Faire, or something else entirely – will be finished in the few days before her appearance as a presenter at the 50th Grammy Awards this Sunday [February 10] at Los Angeles’ Staples Centre, after which she’ll fly to Australia for shows in Perth, Melbourne, Sydney and finally Brisbane.

“My life is so retarded,” she says in that thick, nasally Brooklyn accent. “I look around and go, ‘Where’s the camera? Are we getting punked?’” She laughs. “I lay my gym clothes out, take the kid to school, then I gotta be back for the Russian trainer, who says,” – Lauper switches to a brusque Russian accent – “‘I am going to kick your glutes!’”

The pop star who shot to fame with Girls Just Want To Have Fun in 1983 still makes a new album every few years. She is still beloved by critics for her vocal range and branching out from singing and songwriting to playing instruments and co-producing her work. Audiences can expect all the old hits "but I'll sneak a few new songs in if I can," Lauper says.

The 54-year-old singer-songwriter’s husband, the occasional Law and Order actor David Thornton, has been on location in Serbia playing a cynical New Yorker in the film Here and There – in which Lauper has a minor role – and should be home around mid-week.

Meantime, Lauper has meetings with a stylist to discuss clothes and a trip to the CD store to seek inspiration for an album cover. Not to mention dinners with and reading to Declyn, who was named after Declan MacManus, aka Elvis Costello.

Declyn has recently “turned on” his mother to hip-hop via songs he downloaded and which they sing together in the car. Long enamoured of children’s jump rope chants, Lauper has written one hip-hop number for her new album that began with herself and her drummer; her ambition was to “sing like a drum”.

“But I’m not a rapper,” she concedes. “I hate the way I speak; I hate the fact that I have a really bad accent. You know, I can’t stand my speaking voice.”

Isn’t that what makes her so distinctive? “For you!” she laughs. “For me, it’s horrifying!”

Lauper’s new CD, her first with all-new material since Shine in 2001, is due out in less than a month. Midnight has passed, yet still she talks, and talks. Thank goodness she has a Russian trainer to kick her glutes into action each morning.

It’s hard to imagine Lauper carrying out the instructions of anyone else these days. For her last album, she had wanted to make a blues record, but Sony pressured her for an “unplugged” CD of her greatest hits. The Body Acoustic, released in 2005, was a subdued but sweet reinterpretation of the likes of She Bop and Time After Time, on which Lauper simultaneously sang and played dulcimer and guitar while Sarah McLachlan and Ani DiFranco guested on vocals.

Such collaborations made the project “bearable”, even helped her develop as an artist, Lauper says, “but now it feels like I’m not going to listen to anyone again. I’m going to do just what I want to do”.

The as-yet untitled new album has enlisted UK electronic dance duo Basement Jaxx – “two Mad Hatters, bright and off-centre and kooky and fabulous” – as well as another UK electronic producer duo, Digital Dog, and Swede Peer Astrom, producer for Celine Dion and Enrique Iglesias. Yet this will not be the straight-out dance record Sony originally envisioned.

“I wanted to sing rhythm, not to remix my voice into a rhythm,” Lauper explains. “So it’s rhythmic singing, and there are stories within the songs.” It’s a “collage” collaboration: “I don’t let people take my voice and mechanically manipulate it,” she says.

Not everyone sees things Lauper’s way. Junior Vasquez, co-producer of Lauper’s critically lauded but commercial fizzer Hat Full of Stars album of 1993, told New York magazine last year: “Cyndi Lauper and I are great friends and I think she’s immensely talented, but she’s a control freak with bizarre ideas. She’s a royal pain in the ass to work with.” Perhaps Vasquez should have listened to Girls Just Want To Have Fun: “Some boys take a beautiful girl,/And hide her away from the rest of the world/I wanna be the one to walk in the sun”.

Lauper says Vasquez is “sweet” and a friend, but producers like him “don’t work with artists. They work with people who come in, they tell ‘em what to think, and they go. They’re the king. But I was doing a co-production with him, and that’s completely different. And honey, you’d better be in control of your own project, because if you’re not, who the fuck is?

“What he hated was my playing the dulcimer. And I said something to him about his personal life that he perhaps thinks I shouldn’t have said. I tried to call him, and he didn’t call me back. So I started playing the dulcimer on his answering machine. I thought it was funny, and obviously he didn’t.

“When I look back, I see all these guys who weren’t used to a woman saying, ‘I have this idea’. Well, I’m sorry, turn the album on the front cover and see whose picture is on it and what’s the big name, right? I mean, would he say that about David Bowie?”

Lauper will be in Sydney performing during the week of the Gay and Lesbian Mardi Gras parade. Human rights have always been important to Lauper, raised by a divorced, working-class mother in Brooklyn, among a neighbourhood of “Shakespearean, happy, nutty, sad” people that influenced her unique sense of dress and style.

Lauper almost sounds disappointed that she’s heterosexual. “When I was a kid, all my friends had come out. I thought I was gonna be just like all my friends. Then when I wasn’t, it was weird for me. I had to tell them I was straight.”

In the 1990s, Lauper’s older sister Ellen came out. “With Ellen and my friends, all the people I loved when I was growing up, I got to see discrimination first hand, not just because of the colour of your skin, but because of your preference.”

Lauper once said: “Personally I hope God is a drag queen, so we have a lot to discuss about fashion, makeup and cleavage.” She says now that comment was aimed at “bigots” in a “cookie cutter” society who “stand with the status quo and point at someone who’s not in step”.

Lauper has performed at various Gay Pride events in the US, and in 2007 headlined the inaugural True Colours tour of the US and Canada, alongside Deborah Harry and Margaret Cho, in support of human rights campaigns.

“I always say to Declyn it’s great when you see somebody that’s different from you. I always count my blessings when I do, because if there wasn’t someone who was different from me there would be this uniformity that everyone has to conform and be the same thing; dress the same way, wear their hair the same way. That’s what its almost become now.

“But thank goodness people are different because otherwise it would be a really boring, scary world.”

Cyndi Lauper plays Sydney's State Theatre on February 29, March 1 and 2.