Khrushchev’s secret speech, given to party officials but not published for the general public, showed his desire for de-Stalinization. Basically, Khrushchev has the same criticisms about Stalin that the rest of the world had: he was paranoid, rude, and killed too many people. Khrushchev believed that Stalin had given the world a bad example of socialism. He also stated that many innocent lives had been lost.
When Khrushchev is speaking, he is careful to maintain the language of the party. He emphasizes the point that Lenin didn’t like Stalin. If Lenin, who cannot be wrong, disliked Stalin, than logically this must mean that Stalin was a bad person. Since Lenin expressly stated he did not want Stalin to be the next leader of the USSR, then Stalin’s reign could be viewed as a mistake and a break away from communism. Khrushchev makes it seem as though a communist must choose between Lenin and Stalin. And a good communist will always choose Lenin.
My questions after reading the speech were these: Did Khrushchev dislike Stalin because Lenin disliked him? Or was this speech, as I suspect, a cleverly designed mask for deeper feelings? Did Khrushchev dislike Stalin for the obvious, ethical reasons? Or personal reasons? Whatever the reason, conditions in the Soviet Union began to improve under de-Stalinization.
I would venture to say that Khrushchev looked for an excuse to redirect Stalinism. True, Lenin did not endorse Stalin, but if I recall correctly — not many did. Stalin muscled his way toward the role of Party Head Secretary, eliminating much of the competition. So, it is not so much that Lenin was the cause and support for the speech but, as you hint at, Khrushchev acknowledges the need to revise policy. And Lenin was a step in the right direction, or at least a step away from violent Stalinist policies.