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Lazarus was expected to enter her plea, but the judge announced that the arraignment hearing would be continued to July 6.
The prosecutor issued a felony complaint on Tuesday morning, count one reading as a crime of deliberate and premeditated murder committed by Lazarus, who the prosecution said "unlawfully and with malice murdered Sherri Rasmussen."
The complaint originally read "attempted to murder," but the prosecutor requested the word "attempted" be stricken entirely from the complaint.
Tuesday's court proceeding was the first time the public saw the detective since her arrest.
Police linked Lazarus to the 23-year-old cold case after her DNA matched DNA taken from the scene of a 1986 cold case murder.
Lazarus is charged with murder, with the special circumstance of murder in commission of a burglary. The special circumstance will allow prosecutors to seek the death penalty.
Lazarus has been with the LAPD since 1983.
Sherri Rasmussen, 29, was found beaten and shot to death on February 24, 1986, inside her Van Nuys condominium.
Police believe Lazarus killed her over ex-boyfriend John Ruetten, who had split from Lazarus and married Rasmussen.
Lazarus had gone for years living in her quiet Simi Valley neighborhood, never a suspect in the case. At one time, the LAPD detective was mentioned in the original homicide case because of her relationship with Ruetten, but Lazarus wasn't considered a suspect because investigators believed Rasmussen was a victim of armed robbers.
It wasn't until a saliva sample matched DNA evidence in the cold case from bite marks left on Rasmussen's body.
Her neighbors said they were shocked by the arrest of a woman they've known for years as a dedicated officer.
"I like Stephanie, I've known her for a long time. I've lived here for 30 years, and I feel bad about her," said neighbor Hurlee Inhelder.
"She's a nice person, and I can't believe this," she said.
Lazarus' husband is also a police detective who works out of the San Fernando Valley. Police said he knew nothing about his wife's alleged past.
Lazarus is being held without bail at the Los Angeles County Jail.