The case captivated the US in the 1990s because of the brothers' wealth and privilege as the sons of a record company and entertainment industry executive. A recent Netflix documentary series raised new evidence and revived public interest in the case.
That evidence supported their claims they were sexually abused by their father for years, leading the outgoing district attorney to support their release.
However, with so many people hoping to get inside the courtroom, staff were forced to issue lottery tickets to the crowd as there were only 16 seats inside the courtroom.
A deputy then read out the winning numbers prior to the start of the hearing.
Defence lawyers sought to reduce their first-degree murder conviction to voluntary manslaughter, which could make them eligible for release. The brothers followed the proceedings from prison by audio link, after a video link failed.
The judge rescheduled the hearing for January 30 and 31, 2025, but still decided to hear the testimony of two Menendez relatives - the older sisters of Jose and Kitty - who support the release of the brothers, now 56 and 53.
A separate hearing on re-sentencing that had been requested by prosecutors and scheduled for December 11 was cancelled and will be folded into the January hearing, the judge said.
Los Angeles County District Attorney George Gascon said the new evidence combined with a more modern understanding of sexual abuse led him to ask for re-sentencing of the brothers, saying they had paid their debt to society.
But Gascon was later defeated in the November 5 election and will leave office on December 3.
Incoming District Attorney Nathan Hochman has yet to take a position on the case
Gascon has said there is no doubt the brothers killed their parents but cited a recently surfaced letter Erik Menendez purportedly wrote to a cousin eight months before the murders in which he referred to the abuse.
Investigators also are examining allegations by a member of the 1980s pop band Menudo who said he was abused by Jose Menendez. Those allegations were publicised in 2023 in the documentary series Menendez + Menudo: Boys Betrayed.
Had the evidence been presented at trial, the jury may have reached a different outcome, Gascon said.