Mrs White was at home with her 11-week-old son Shane on June 8, 1973, when a man burst into her unit in Coogee in Sydney's eastern suburbs.

The 26-year-old was forced to undress before the man stabbed her in a frenzied attack in the hallway. Shane was in his cot less than one metre away.

Mrs White's then-husband, Paul White, arrived home several hours later to find her body.

The cold-case investigation was reopened in recent years and uncovered fresh DNA evidence.

New details to be aired on the ABC's Australian Story program on Monday night reveal Mrs White confided in her friends about being followed and having a man expose himself at her front door.

Writer and friend Bob Wurth said Mrs White started receiving obscene phone calls "out of the blue" that got more and more depraved.

"It was a young bloke saying things like 'I'm coming to get you, I know where you live,' " he told Australian Story.

"And then he referred at one stage to 'I've got a white coffin for the baby.' "

On another occasion, Mrs White responded to a knock at her front door, peered through the eyepiece and saw a man standing on the other side.

Mr White said the man flashed himself in front of her.

"I don't think she knew him," he said.

The investigation has been frustrated by the fact that crucial pieces of evidence were lost, including a nappy the killer may have used to wipe blood off himself, DNA swabs and a knife.

After Mrs White's death, police released a sketch of a man seen leaving the Beach Street unit block about the time of the killing.

Detective Senior Constable Deon Kelly said police also received an anonymous phone call and letter about a man holding a towel to his head, spotted leaving the driveway of the unit block.

"To this day they remain anonymous but they've actually witnessed some very important details including the registration of the vehicle," he told Australian Story.

Senior Detective Kelly said there were also a few instances in which Mrs White was followed after she finished performing in shows as a hula dancer.

"But there's also the possibility of it being the same person responsible for the phone calls or the indecent exposure at her unit," he said.

Another lead police are pursuing relates to someone who came to Mrs White's unit and "suggested they go to bed together".

That person was involved with a cleaning product company for which Mrs and Mr White were managers.

"Lyn has told the person to never come back and she hasn't really, as far as we can tell, identified to anybody who it was," Senior Detective Kelly said.

Fairfax Media reported last year that unsolved homicide team detectives returned to the unit.

They ripped back the carpet and found a bloodstain on the concrete.

Mrs White's DNA profile and two male profiles were found in the stain.

Anyone with information is urged to contact Crime Stoppers on 1800 333 000.

Murder by the Sea: The Lynette White Story airs on the ABC's Australian Story at 8pm on June 5.