Stephen, a bright, popular, 18-year-old student, was stabbed to death at a bus stop in Eltham, south-east London, by a gang of white youths in April 1993. Nobody has been convicted of the murder.
The officer involved has not been suspended or named, nor the rank revealed, and Scotland Yard was last night considering if the individual would face an internal disciplinary board.
The board has a wide range of options to consider if the officer was disciplined, including dismissal from the force.
The PCA stated: "Authority member Ms Joe Dobry has recommended that one senior officer who is still serving with the Metropolitan Police service should face a charge of neglect of duty."
The PCA investigation started in spring last year following the inquest into Stephen's death that found he was unlawfully killed in a racially motivated attack by five white youths.
The Lawrence family called for an investigation into the police handling of the case and a report on the investigation was published last December.
A spokeswoman for the Metropolitan Police said last night: "We have received their recommendation and the matter is under discussion. This is being considered by the Metropolitan Police Service. If necessary, the authority has the power to direct the Metropolitan Police Service to charge the officer."
Stephen's father, Neville Lawrence, said the news was a small step in the right direction, but not enough. "One of the main things I have said all along is that when I feel vindicated is when somebody's doing time, and that's the only time I am going to feel vindicated in any way," he told the BBC's Six O'Clock News.
A member of the Stephen Lawrence campaign, Mrs Ros Howells, added: "We have always known that the police failed. It's a pity that it's just one police officer and the others have retired, but we think it's great news."
"I think this has come as quite a shock to Doreen Lawrence. But five years on we will never feel good until the perpetrators of the crime are behind bars."
It is unusual that the Lawrence family has been informed of the PCA's recommendation before the Metropolitan Police have had a chance to consider it, but this move highlights the high profile that the case has taken. The Stephen Lawrence Campaign has petitioned constantly during the years since Stephen's death for justice, often in the face of seemingly impossible odds.
A source at the PCA said: "This has been forced upon us by the demands of the inquiry.
"We decided it was important that all officers should know whether they faced disciplinary charges. We also felt that if the officers knew, the family should know too."