It is not believed that either culprit was hit, police told the Times.
Sources did not reveal the names of the officers nor how many shots were fired by one or both of them.
There were also no reports to suggest that the suspects returned fire.
Lacey recently lost her reelection bid to challenger George Gascón, a reform candidate who promised compassionate leadership at the nation’s largest municipal prosecutor’s office.
»PREVIOUS COVERAGE: LA district attorney defeated in reelection bid
Lacey, 63, conceded the race after failing to garner more than two-thirds of the remaining tally to be reelected.
»FROM MARCH: LA district attorney headed to victory days after protesters held at gunpoint
Her eight-year tenure may have come to an end in part because of the anti-law enforcement sentiments that swept the nation in the aftermath of George Floyd’s death.
More than 500 fatal police shootings were reported under Lacey’s watch since she was first elected in 2012. Reports say she has declined to bring charges in most if not all of the cases.
»PREVIOUS COVERAGE: District attorney apologizes after Black Lives Matter protesters held at gunpoint
Police brutality became a critical focus of the race. During the primary election in March, Lacey finished far ahead of Gascón and former public defender Rachel Rossi.
But after Floyd’s death, Gascón found momentum amid protests calling for changes to the criminal justice system.
He will take over the nation’s largest prosecutor’s office in January.