A mind flayer who decided to follow the path of wizardry could achieve a lesser form of lichdom and become an undead creature known as an alhoon. It was also possible, although rare, for an extremely powerful mind flayer wizard to become a true lich, also known as an illithilich. These terrible beings were so rare that usually people did not make that distinction.

https://www.youtube.com/watch?v=Vsl2_bRhcY0