Erik and Lyle Menendez's relatives aren't saying much about their first meeting with the new L.A. County District Attorney Nathan Hochman ... but he's about to hold a news conference where we could finally learn where he stands on the case.

We caught up with the Menendez Brothers' attorney, Mark Geragos, and their loved ones outside the Hall of Justice in downtown L.A. ... moments after they tried to convince Hochman to get onboard with letting Erik and Lyle's out of prison where they've been serving their life without parole sentences for the 1989 shotgun murders of their parents Jose and Kitty Menendez.

We asked Geragos if he and the family had been successful in their mission to make the D.A. see the case their way -- but no one wanted to comment.

In the decades since, the siblings' loved ones have formed the Justice for Erik and Lyle Coalition in the hope of getting them released from prison ... with the family noting the brothers have been rehabilitated following their nearly 35 years behind bars.

We also got the Menendez fam earlier Friday on their way into the meeting with Hochman, but they were equally reticent about the case.

We're expecting D.A. Hochman to say more about the meeting shortly. He's scheduled a news conference for 4:30 PM PT ... and we'll be live streaming it here in this post.

Of course, former L.A. County D.A. George Gascón supported a resentencing for the brothers, noting they've been model inmates during their time in prison.

However, after Gascón lost his November reelection bid to Hochman, Erik and Lyle's initial hearing on the matter was delayed to 2025.

Since taking office, Hochman has not made it clear where he stands on the issue ... though, he did meet with a lawyer of one relative who does not support Erik and Lyle's release.