LOS ANGELES—A former Los Angeles Police Department civilian employee was sentenced Jan. 17 to two consecutive life prison terms without the possibility of parole for murdering his wife and teenage son as they slept in their Van Nuys apartment.

Viktor Yuryevich Glukhovskiy—who worked in the LAPD’s Security Services Division—was convicted last November of the Dec. 26, 2018, killings of his wife, Natali, 39, and their 13-year-old son, Alex, who were each shot in the head in their beds in the family’s second-floor apartment in the 13800 block of Oxnard Street.

Jurors found true special circumstance allegations of lying in wait and multiple murders and gun use and discharge allegations, but rejected a special circumstance allegation of murder for financial gain. Prosecutors had suggested the killings were done in part to cash in on insurance policies, but also so Mr. Glukhovskiy could begin a new life with another woman.

“To kill one’s spouse is atrocious. To kill one’s child—a blood son—is unimaginable,” Los Angeles County Superior Court Judge Ronald S. Coen said just before handing down the sentence.

Three people who spoke on the victims’ behalf said they are still grieving the deaths.

“Her murderer did not just kill two people. He hurt so many,” Yelena Kaminsky told the judge. “The cruelty of what happened to Natali and Alex reaches a completely different level ... This is beyond betrayal. This is pure evil.”

Another friend, Marie Morgan-Haberman, said the victims were “two beautiful people who had so much ahead of them.”

“There is no forgiveness here,” she said, adding that the defendant is “going to get exactly what he deserves.”

Mireille Rostamian told the judge that “the heartbreak will never go away.”

In a sentencing memo, Deputy District Attorney Dan Akemon wrote that Mr. Glukhovskiy “ambushed” his wife and son “in their beds as they slept, and shot them in the head with an improvised shotgun, killing them both.”

The prosecutor told jurors during the trial that it was “a case about a family annihilated.”

The deputy district attorney said Mr. Glukhovskiy had a “dark secret” that he was in love with another woman, was “willing to murder” to be with her, and had been plotting the killings for months.

Mr. Glukhovskiy left the apartment that morning, turned off his cell phone to try to conceal his whereabouts, circled back in his distinctive white Jeep that was seen on surveillance video, and changed his clothing and donned a hoodie and gloves after parking in the neighborhood, the prosecutor told jurors.

Mr. Akemon told the panel that the gait of a hooded man who was seen on surveillance video walking outside the apartment complex early that morning is “identical” to the way the defendant is seen walking in surveillance footage subsequently taken in January 2019 at Hollywood Park Casino.

The prosecutor said the evidence would show that Mr. Glukhovskiy killed his two family members before driving to his job in downtown Los Angeles, where he showed up to work 15 minutes late and “acted like nothing happened.”

Mr. Glukhovsiky called 911 after returning home late that night and “acted like a grieving husband and father” and then subsequently lied to police about the state of the couple’s failing marriage and concealed his relationship with his girlfriend, according to the prosecutor.

The prosecutor said Mr. Glukhovskiy and his girlfriend, who was from Ukraine and was living in Poland at the time, were engaged to be married while he was still married to his wife. Mr. Akemon told the panel the defendant sent messages to his girlfriend including one in which he wrote that she was “the only woman I care about.”

Mr. Glukhovskiy filed a claim for two insurance policies worth more than $400,000 involving his wife and son after their deaths, according to the prosecutor.

He denied killing his wife or son when he was questioned again by Los Angeles Police Department detectives shortly before his arrest Feb. 1, 2019.

Defense attorney Greg Hoegee told jurors he believed the evidence pointed to his client’s innocence.

He noted there was “blood everywhere” at the crime scene, and said police criminalists took samples from Mr. Glukhovskiy’s vehicle.

“They didn’t find anything that would tie Mr. Glukhovskiy to the crime scene,” Hoegee said.

He said the prosecution asked the jury to make inferences that are “not reasonable.”

The defense lawyer said it was “not a reasonable inference” that his client was the one who committed the crime.

Mr. Glukhovskiy’s attorney told the panel that he likes to look at the case as a “big, giant puzzle,” telling jurors that the puzzle pieces “aren’t there” or “just don’t fit.”

Mr. Glukhovskiy has remained behind bars since his arrest.