When you cast a spell it checks target and then decides what happens. Willing is the most restrictive of the various subsets in targets (everything but objects falls into the creature subset, for example; or everything that is undead falls into the undead subset, which is a part of the creatures subset. So a lich would fall into the Creature (Undead (Intelligent Undead)) set.
The bottom of the set is willing; you become part of that set in only 2 situations, if you choose it or if you are unconscious. Everything that is part of the willing subset gets no save.