Final answer:
The CN V1 (Trigeminal nerve, Ophthalmic division) supplies sensory input to the eyeball and the skin of the lateral nose, upper eyelid, and anterior scalp.
Step-by-step explanation:
The nerve that provides sensory supply to the eyeball and cutaneous branches that supply the skin of the lateral nose, upper eyelid, and anterior scalp is the CN V1 (Trigeminal nerve, Ophthalmic division). This nerve is part of the trigeminal nerve, which is responsible for cutaneous sensations of the face and is also involved in controlling the muscles of mastication. The trigeminal nerve has three divisions: ophthalmic, maxillary, and mandibular, with the ophthalmic division (CN V1) specifically supplying the areas in question.