**Core Concept**
Lesions affecting the oculomotor nerve (CN III) or the frontal eye field (Brodmann area 8) can result in impaired lateral gaze. However, the specific pattern of gaze palsy depends on the location and extent of the lesion.

**Why the Correct Answer is Right**
The correct answer is related to the anatomy of the frontal lobe, specifically the frontal eye field (FEF). The FEF, located in the premotor cortex, plays a crucial role in controlling voluntary eye movements, including lateral gaze. Lesions in this area can result in ipsilateral conjugate gaze palsy, meaning the affected eye is unable to move in the direction of the lesion. This is because the FEF sends signals to the ipsilateral oculomotor nerve (CN III) to move the eye laterally. Damage to the FEF disrupts this pathway, leading to impaired lateral gaze.

**Why Each Wrong Option is Incorrect**
**Option A:**
This option is incorrect because lesions of the oculomotor nerve (CN III) would result in vertical gaze palsy, not lateral gaze palsy.

**Option B:**
This option is incorrect because the parietal lobe is involved in spatial attention and processing, not eye movement control.

**Option C:**
This option is incorrect because the occipital lobe is involved in visual processing, not eye movement control.

**Clinical Pearl / High-Yield Fact**
When evaluating patients with gaze abnormalities, it's essential to consider the location and extent of the lesion, as well as the specific pattern of gaze palsy, to determine the underlying cause.

**Correct Answer: C. The frontal eye field (Brodmann area 8).**