SAN FERNANDO, Calif.—An ex-con was found guilty on Aug. 25 of first-degree murder in a retrial stemming from the killing of a Los Angeles Police Department (LAPD) officer during a traffic stop in Lake View Terrace more than 40 years ago.

The jury in San Fernando was the third to hear the case against Kenneth Earl Gay, now 65, who was charged with murder for the June 2, 1983, shooting of Officer Paul Verna, a married father of two sons who both eventually became police officers.

Jurors also found true special-circumstance allegations of murder of a peace officer in the performance of his duties and murder to avoid or prevent a lawful arrest.

The panel could not reach a unanimous verdict involving an allegation that Mr. Gay personally used a gun during the crime.

Mr. Gay’s conviction had been reversed once by the California Supreme Court, and his death sentence has been reversed twice.

Most recently, the California Supreme Court sent the case against Mr. Gay back for retrial in the guilt phase, finding that he was “denied his constitutional right to the assistance of competent counsel” during his first trial.

The L.A. County District Attorney’s Office had opted against seeking the death penalty in the retrial after District Attorney George Gascón was elected.

Superior Court Judge Hayden Zacky had rejected a bid by Mr. Gascón’s office in January 2021 to dismiss the two special circumstance allegations under which Mr. Gay is now facing life in state prison without the possibility of parole. Mr. Verna’s widow and two sons also spoke out against the dismissal.

Mr. Gay—who appeared in court in a wheelchair throughout his trial—is due back in court for sentencing on Oct. 2.

The latest jury had deliberated over portions of a period of two weeks, during which one juror was replaced and the panel was ordered to begin deliberations anew.

Sandy Jackson, Mr. Verna’s widow, who has since remarried, said after Friday’s verdict that it was “agonizing” the jury was out so long.

“The end result is what it should be,” she said. “He should not be out among us.”

Mrs. Jackson said she had been “hoping that the third time is the charm.”

Both of Mr. Verna’s sons went on to become police officers, and one of his sons, Bryce, wore his Los Angeles Police Department uniform—which bears his father’s old badge—to court for the verdict.

In his closing argument, Deputy District Attorney Eric Siddall told the jury that Mr. Verna “had no idea who he was about to encounter” when he pulled over a car containing Mr. Gay, his alleged crime partner Raynard Cummings and Mr. Cummings’ wife, whom he said had “been engaged in a series of violent and brutal robberies” in the San Fernando Valley.

Mr. Verna did not know that there was a gun in the vehicle that would be used for a sneak attack to kill him, but one of his last acts as an officer was to write a ticket, resulting in evidence that would eventually lead to solving his own murder, according to the prosecutor.

Mr. Siddall called the officer’s killing “a brutal murder that was completely consistent” with the brutality they showed each of their victims.

Fellow prosecutor David Ayvazian told jurors that Mr. Cummings fired the first shot at Mr. Verna from the car and that Mr. Gay emerged from the car, shot the officer three times in the back and then shot him twice more as the officer was on the ground dying. It all happened shortly after the two men were paroled from prison.

One of Mr. Gay’s attorneys, Monnica Thelen, told jurors in her closing argument that the case was “severely lacking” and that Mr. Gay had “nothing to do with the murder,” calling Mr. Cummings the “sole killer” and saying that the person who was responsible had “already been held accountable.”

The defense lawyer said it was “ludicrous” to think that Mr. Cummings would turn his back after firing the first shot at Mr. Verna and pass the gun to Mr. Gay.

“They were going to hold both of these men accountable,” Ms. Thelen told jurors in her closing argument.

Mr. Gay’s attorney urged jurors not to allow “some brutal evidence of robberies” to inflame their passions.

During the third trial, Mr. Cummings’ ex-wife, Pamela Smith, was called as the prosecution’s first witness and identified a photo of Mr. Verna as the man who was murdered.

“Who murdered him?” Mr. Siddall asked.

“Kenny Gay,” she responded.

“Anyone else?” the prosecutor again asked.

“Raynard Cummings,” she added.

Mr. Gay’s case was sent back to the San Fernando courthouse after the California Supreme Court ruled in February 2020 that he was “denied his constitutional right to the assistance of competent counsel” during the guilt phase of his trial.

Earlier, the California Supreme Court had twice overturned Mr. Gay’s death sentence.

Mr. Gay’s first death sentence in 1985 for Mr. Verna’s killing was overturned in 1998, with the California Supreme Court finding that he had not received “constitutionally adequate representation” during his first trial. A retrial was ordered for the penalty phase of his case.

When he was sentenced a second time to death in December 2000, Mr. Gay maintained he “never murdered anyone.”

“What this decision really was, was an insult” to the Verna family, Gay said then, while turning to look at the LAPD motorcycle officer’s widow and two sons. “It has been 17 years and you folks still haven’t heard the truth about what happened to your loved one.”

The defendant said then that he would admit it if he were responsible for Mr. Verna’s killing and that he owed the slain officer’s family an apology for not having the courage to stand up to Mr. Cummings, who was also sentenced to death for the officer’s slaying.

Superior Court Judge L. Jeffrey Wiatt, who presided over Mr. Gay’s second trial, said when he sentenced Mr. Gay in December 2000 that he didn’t think there was any question that Mr. Gay fired the final five shots at Mr. Verna.

In 2008, the California Supreme Court again overturned Mr. Gay’s death sentence, finding that Judge Wiatt had erred by barring Mr. Gay from offering “significant mitigating evidence” during the penalty phase of his retrial, including four statements in which Mr. Cummings claimed that he was the sole shooter.

Mr. Cummings was convicted of first-degree murder and sentenced to death in 1985 for Mr. Verna’s killing. The California Supreme Court subsequently upheld his conviction.