Can you have cranial nerve damage with face lacerations?

Yes: You can easily have injury to the facial or trigeminal nerve with facial lacerations. Other cranial nerves can also be involved, though these are the cutaneous nerves, and more easily damaged with superficial injuries.

Yes: If a cranial nerve is injured in the face, it is usually either the trigeminal (#5) or facial (#7). Depending on where the laceration is, sometimes these nerves require repair, other times they can be left to re-sprout in the area.

See details: I am not sure there is anything you can do. Discuss the issue with a neurologist.