Ok, we all know USSR just couldn't win the moon race, at least they could not land, not with this monster N-1 rocket.
But whatif they had circle the moon before Apollo 8, around september 1968 ?
Let's suppose that Korolev survive surgery in january 1966. Then early Soyuz flight are less disturbed, Komarov fly later but at least he survive. This, and Korolev charisma and caracter strong enough to resist pressure from the Party allow a much more reliable Zond spacecraft.
Thus Leonov and its mate circle the moon before Apollo 8 in august 1968.
Ok, they can't even enter orbit, but how would this impact Apollo ?