Clue is an artifact type. Even though it appears on some cards with other permanent types, it's never a creature type, a land type, or anything but an artifact type.

If the target of Lazav, Wearer of Faces's first ability is illegal as the ability tries to resolve, it won't resolve and none of its effects will happen. You won't investigate.

You can't sacrifice a Clue to pay multiple costs. For example, you can't sacrifice a Clue token to activate its own ability and also to activate Alquist Proft, Master Sleuth's ability.

Some spells and abilities that investigate may require targets. If each target chosen is an illegal target as that spell or ability tries to resolve, it won't resolve. You won't create any Clue tokens.

Some abilities trigger "whenever you sacrifice a Clue". Those abilities trigger whenever you sacrifice a Clue for any reason, not just to activate a Clue's activated ability.

If an effect refers to a Clue, it means any Clue artifact, not just a Clue artifact token. For example, you can sacrifice Wrench to pay for Alquist Proft, Master Sleuth's activated ability.