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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." Play video content

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 nons

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