By the time of Lenin’s death his wishes did not play a major role and, anyway, it is not like he left a clear “successor”. And what “successor” means to start with? Formally, Lenin was just a Prime Minister and the most influential member of Politburo in which he did not held any special position (aka, was not officially a “Fearless Leader”). Stalin became PM only in 1941. He also managed to elevate his office of the Secretary General into the most powerful position in the SU: under Lenin there was not official head of the Party. So by the end of Lenin’s life Stalin already controlled most of the communist nomenclature and had a number of allies in Politburo thus making Lenin’s wishes rather irrelevant. Of course, he was not, yet, in a dictatorial position but he was one with a powerful tool in his disposal.