Cooper Koch is up for an Emmy for portraying Lyle Menendez in “Monsters: The Lyle and Erik Menendez Story” … and, he shared a message from the man himself on the awards show red carpet.

The actor told Variety on the red carpet … Lyle did reach out to him before the Emmy Awards with a sweet message — but, also reminded him not to make it about the accolade.

Koch says Lyle told him, “All that matters is the awareness.”

As you know … the Menendez brothers were denied parole last month in a hearing which their lawyer Mark Geragos referred to as “rigged” on our “2 Angry Men” podcast.

Geragos says the parole board completely ignored Erik and Lyle’s good deeds … while focusing on cell phone infractions — and other issues he considered nonsensical.

Lyle could receive another parole hearing in as soon as 18 months … but, it was obviously a blow to both himself and Erik.

BTW … “Monsters: The Lyle and Erik Menendez Story” received two Emmy nominations — one for Koch and the other for Outstanding Limited or Anthology Series