Cold-case detectives arrested her June 5 while at work with the LAPD's Art Theft Unit.
Police say the DNA evidence linked Lazarus to saliva from bite marks on the victim Sherri Rasmussen, who was 29 when she was killed.
Rasmussen was shot and killed in 1986. The weapon used in her murder was never found.
However, shortly after the murder, Lazarus reportedly contacted the Santa Monica Police Department to report a theft from her car, including personal items and a gun.
Investigators believe that gun was used to kill Rasmussen.
According to LAPD Deputy Chief Charlie Beck, Rasmussen's body was found by her husband, John Ruetten, in their Van Nuys condominium.
Beck said Ruetten had a long-term relationship with Lazarus prior to his marriage.
Prosecutors are expected to decide later whether to seek the death penalty against Lazarus.
Lazarus is set to appear for a preliminary hearing July 21 at the downtown L.A. Courthouse.
City News Service contributed to this report.