I agree with Lilo that Fredo did not committ Mike's attempted murder. I believe that he unknowingly facilitated it. He was a dunce on both sides the equation. He was incapable of handling something as complex as a murder; he was also incapable of handling the pathos associated with such facilitation and figuring out the important angles.

On the other hand, while Lansky did have associates who may have acceded to his suggestion that someone be murdered, Lansky did not have an organization with him at its pinnacle from where he dished out life and death.