**Core Concept**
Lateral Medullary Syndrome, also known as Wallenberg's syndrome, is a neurological disorder caused by a stroke or infarction in the lateral part of the medulla oblongata. It involves damage to the nuclei and fibers of the cranial nerves that arise from the medulla.

**Why the Correct Answer is Right**
The correct answer is **D. XII CN** because the Hypoglossal nerve (XII CN) is not typically affected in Lateral Medullary Syndrome. This is because the hypoglossal nerve nuclei are located in the rostral (upper) medulla, outside of the typical area affected by the stroke or infarction. In contrast, the nuclei and fibers of the Vth (Trigeminal nerve), IXth (Glossopharyngeal nerve), and Xth (Vagus nerve) cranial nerves are commonly involved in Lateral Medullary Syndrome due to their close proximity to the lateral medulla. The damage to these nerves can result in a range of symptoms, including dysphagia, hoarseness, and difficulty swallowing.

**Why Each Wrong Option is Incorrect**
**Option A:** The Vth CN (Trigeminal nerve) is often affected in Lateral Medullary Syndrome, leading to symptoms such as ipsilateral facial weakness and contralateral loss of pain and temperature sensation in the face.
**Option B:** The IXth CN (Glossopharyngeal nerve) is also commonly involved, resulting in symptoms such as dysphagia, dysphonia, and a diminished gag reflex.
**Option C:** The Xth CN (Vagus nerve) is frequently affected, leading to symptoms such as hoarseness, dysphonia, and difficulty swallowing.

**Clinical Pearl / High-Yield Fact**
In Lateral Medullary Syndrome, the pyramidal tract is often spared, which is why motor weakness is typically not a prominent feature. However, the involvement of the spinal trigeminal nucleus and tract can result in pain and temperature sensation deficits in the face.

**✓ Correct Answer: D. XII CN. The Hypoglossal nerve (XII CN) is not typically affected in Lateral Medullary Syndrome.**