Lazarus pled not guilty to the crime.
The first witness called Monday was retired Los Angeles County coroner's criminal specialist Lloyd Mahanay, who testified that he took a swab from a bite mark found on the victim's left arm.
Authorities say DNA from that saliva links Lazarus to the body.
Rassmussen's husband of three months, John Ruetten discovered her body at the condo.
Authorities say he had been involved with Lazarus before he married Rassmussen.
Lazarus was mentioned in the 1986 case file, but was not a suspect because detectives believed two robbers, who had attacked another woman in the area, were behind the murder.
Her defense attorney, Mark Overland, had earlier motioned to have the charges dismissed, arguing her right to a fair trial was violated because LAPD investigators were negligent and showed carelessness in the probe of their colleague.
Superior Court Judge Robert Perry denied that request.
"I don't think, based on these papers, there was reckless disregard of Ms. Lazarus's due process of rights," Perry said.
Lazarus has been in custody since June, when she was arrested by detectives who worked across the hall from her.
The murder charge includes the special circumstance allegation of murder during a burglary.
Lazarus also faces a separate charge, of personal use of a handgun.
It was still unclear Monday, if prosecutors would seek the death penalty.
AP contributed to this report.