**Core Concept**
The question requires knowledge of the cranial nerves and their respective functions, specifically the extrinsic eye muscles. The lateral rectus muscle is one of the six extraocular muscles responsible for eye movement.

**Why the Correct Answer is Right**
The abducens nerve (Cranial Nerve VI) is responsible for the motor innervation of the lateral rectus muscle. This nerve arises from the brainstem and courses through the cavernous sinus before exiting the skull through the superior orbital fissure. Upon entering the orbit, it supplies the lateral rectus muscle, which is responsible for abducting the eye (moving it away from the midline). The abducens nerve also receives parasympathetic fibers from the Edinger-Westphal nucleus, which are responsible for pupillary constriction in conjunction with the oculomotor nerve.

**Why Each Wrong Option is Incorrect**
**Option A:** The trochlear nerve (Cranial Nerve IV) supplies the superior oblique muscle, which is responsible for intorsion (rotation of the eye) and depression of the eye.
**Option B:** The trigeminal nerve (Cranial Nerve V) is responsible for sensory innervation of the face and motor innervation of the muscles of mastication (chewing).
**Option D:** The glossopharyngeal nerve (Cranial Nerve IX) is primarily responsible for swallowing, salivation, and taste sensation in the posterior one-third of the tongue.

**Clinical Pearl / High-Yield Fact**
The abducens nerve is unique in that it is the only cranial nerve that is not associated with a specific cranial nerve nucleus within the brainstem. Instead, it arises from the paramedian pontine reticular formation.

**✓ Correct Answer: C. Abducens**