Detective Inspector Ben Bullock, who was second-in- command of the murder inquiry, still faces three further counts at an internal police disciplinary hearing.
Last month the tribunal was given 28 days to complete the hearing before Insp Bullock retires. The three-strong tribunal decided there was "no case to answer" on more than half the charges. The decision to drop them was made yesterday after a submission by his lawyers on Tuesday.
At the opening of the tribunal Glen Smyth, chairman of the Metropolitan Police Federation, which is representing Insp Bullock, described some of the charges as a "desperate" attempt to find wrongdoing.
The charges follow Sir William Macpherson's report into the murder, which accused Insp Bullock of failing to follow up vital evidence on the black teenager's death in 1993.
A Scotland Yard spokeswoman said yesterday: "Following defence submissions on Tuesday, the independent Police Complaints Authority disciplinary tribunal hearing the case against DI Ben Bullock has decided that there is no case to answer on four of the charges of neglect of duty."
Insp Bullock put in his retirement papers on 25 June, at the start of the full disciplinary hearing, giving notice of his decision to leave the force within 28 days. The Metropolitan Police Federation said he had been advised by doctors to quit because of failing health.
He postponed his retirement after 30 years in the Met to contest the case, but in a statement at the beginning of the tribunal said he had become so exasperated with delays and legal challenges by the Lawrences' lawyers that he was giving notice to retire.