Phil Ormsby says his one-woman play, Drowning In Veronica Lake, began with a case of mistaken identity. He hadn't originally set out to write about Veronica Lake.

"I confused her with someone else ... Lana Turner," Ormsby says.

"When I started reading about her, I thought, 'Oh, she's way better!"'

Ormsby had wanted to write a play using the story of an old-time Hollywood star to explore the ups and downs of fame and found Lake's story compelling.

The resulting play, performed by his partner, Alex Ellis, and directed by Simon Coleman, was first performed in New Zealand at the Auckland Fringe Festival in 2011. It was presented at the Adelaide Fringe a couple of years later and has been picked up for an Australian tour.

In the play, Ellis as Lake is wearing a huge gown that virtually imprisons her on the stage, representing the glamorous prison that fame can be.

Ellis says, "I can't move from the spot."

Trapped in a sort of spiritual green room, the stage Veronica Lake talks about her life and career as she waits for her comeback and it becomes hard to tell just what is fact and what is fiction. And that's by design. Lake was born Constance Ockleman in about 1922. Like so much in her life, including her height (somewhere between 150cm and 155cm) it can be hard to pin down the truth.

While still a teenager, encouraged by her mother, Constance began working as an extra in films and moved up to bit parts and, in 1941, stardom in the film I Wanted Wings. Her peek-a-boo hairstyle was her trademark (although she was reportedly asked to change it during World War II by government officials who feared women adopting it might have workplace accidents). Veronica Lake, as she was renamed, starred in comedies such as Sullivan's Travels (1942) and films noir including This Gun For Hire (1942).

But alcoholism and a reputation for being difficult hindered her career and by the early 1950s she was bankrupt, twice divorced and had been sued by her mother for non-support. She left Hollywood for New York and acted on stage in the US and Britain but at one point was discovered working as a barmaid, much to the shock of fans.

Ellis says, "She and Marlon Brando had been lovers. He sent her a cheque for $1000 but she didn't cash it, she had it framed and had it hanging on the wall."

Another two marriages and divorces followed as well as an autobiography and a couple of low-budget movies before she died in 1973 aged about 50, apparently of hepatitis, estranged from her children.

But there was more to Lake than either the Hollywood sex symbol, or "sex zombie", as she put it, or the unhappy figure of her later years.

Ellis says, "She taught herself how to fly; she was smart, she wasn't a dumb blonde."

Much to the consternation of publicity departments, she would make up things in interviews just to see if she could get away with it, claiming to be studying medicine, for example, which didn't endear her to the Hollywood studio machine.

Ellis and Ormsby heard a rumour that Lake's oldest daughter Elaine had moved to Christchuch in the 1960s. And, Ellis says, "out of the blue came a phone call."

Elaine, who had changed her name and lived out of the limelight, had seen the show.

"She really loved it. We met up with her and had coffee ... She said it was bang-on, [Lake] was horrible. They didn't have a good relationship, which was part of the reason she moved to New Zealand."

Although Veronica Lake has faded from prominence, several of her movies are well-remembered and her image has lived on in films: Kim Basinger's Oscar-winning role as Lynn Bracken in LA Confidential was drawn from Lake's look.

Maybe, Ellis and Ormby say, if Lake had achieved fame a bit later in life or in a more supportive family environment she would have dealt with it better – or maybe she would have been happier without it.