That's the one I was more familiar with. (Is it the same name in some sense? On the one hand it rather looks like two different transcriptions of the same name; on the other hand Illich's father wasn't Russian and the names seem to be written differently in the Russian Wikipedia: Иллич, Ильич.)
Ильич is a patronym (son of Ilya). Lenin's father's first name was Ilya.
It's not clear whether Иллич (pronounced differently) is related, apparently it's used as a given name in some countries, or it might be an unrelated surname, or it might be a misspelling/mistranscription of the Russian patronym. Who knows!
