The same jurors last month found Jade Douglas Harris, 37, guilty of three counts of murder and several other charges including attempted murder and kidnapping.
According to prosecutors, Harris' shooting rampage began after he went to a Downey business on Oct. 24, 2012, in response to a Craigslist ad for a 2010 Chevrolet Camaro.
He shot three people, killing two — Josimar Rojas, 26, and Irene Cardenas Reyes, 35, authorities said.
Then he forced Susana Perez Ruelas, 34, to drive him and her son to a nearby home, where the Camaro was parked. After arriving, he shot and killed Perez Ruelas and wounded her son, prosecutors said.
Harris was arrested a day after the killings. He had been paroled three months before the shootings after being convicted in 2005 of robbery and attempted robbery.
He is scheduled to be sentenced April 21, the Los Angeles County district attorney's office said.
Gov. Gavin Newsom last year announced a moratorium on the death penalty in California. Newsom's reprieve lasts as long as he is governor and does not prevent prosecutors from seeking nor judges and juries from imposing death sentences.