There are various reasons that Stalin pretended that he was close to Lenin. For example, he thought that it would gain him support.
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Joseph Stalin was sometimes called Lenin's left leg as a pun on the description of a close helper as a "right hand man" and because Stalin practically idolized Lenin.
Vladimir Lenin, then Joseph Stalin
At first, lenin... then lenin died and Stalin screwed with the succession and seized power.
Stalin's chief was Vladimir Lenin during the years before the Russian Revolution and until Lenin's death.
Lenin felt that Stalin was far too harsh and that he would not make a good leader, but after his unexpected death in 1924, Lenin did not name his succesor, and Stalin took that chance to take power.