In their bid to seek a new trial or resentencing, Lyle and Erik Menendez have filed a blistering motion to disqualify the office of the District Attorney from participating in the proceedings.

“The record shows a conflict that renders it unlikely Erik and Lyle can receive a fair resentencing hearing, recusal is proper,” the 160-page filing states.

The case involving the famed brothers — who have served 35 years in prison for the 1989 murders of their parents, Jose and Kitty, at their Beverly Hills home — has featured various twists and turns over the past six months. In October, then-District Attorney George Gascón moved to reduce the brothers’ sentence from life without parole to 50 years to life. That reduction, if granted, would make the brothers immediately eligible for parole. But Gascón lost in the November election, and newly elected D.A. Nathan Hochman reversed course and withdrew Gascón’s resentencing recommendation.

“The views...