My own guess is that Lenin's children get honorable but minor jobs (especially connected with libraries, museums, etc. related to their father's memory). None of the Bolshevik leaders will want a Lenin dynasty.
Will they be purged by Stalin? Doubtful. None of Lenin's surviving siblings (Dmitry, Anna, Maria) were purged in OTL, and Krupskaya died a free woman, despite her involvement with the Opposition in the 1920's...