**Core Concept**
Lateral medullary syndrome, also known as Wallenberg syndrome, is a neurological disorder caused by a lesion in the lateral part of the medulla oblongata. This condition typically results from occlusion of the vertebral or posterior inferior cerebellar artery, leading to ischemia and damage to the surrounding brainstem structures.

**Why the Correct Answer is Right**
The clinical manifestations of lateral medullary syndrome are a result of the involvement of various cranial nerves and their nuclei, as well as the spinothalamic tract. The key features include:
* Ipsilateral impairment of the vagus nerve (cranial nerve X), leading to hoarseness and dysphagia
* Ipsilateral impairment of the glossopharyngeal nerve (cranial nerve IX), resulting in difficulty swallowing and a decrease in the gag reflex
* Contralateral impairment of the spinothalamic tract, causing pain and temperature sensation loss on the opposite side of the body
* Ipsilateral Horner's syndrome, characterized by ptosis, miosis, and anhidrosis

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the clinical features of lateral medullary syndrome do not typically include a decrease in the corneal reflex.
**Option B:** This option is incorrect because the involvement of the abducens nerve (cranial nerve VI) is not a characteristic feature of lateral medullary syndrome.
**Option C:** This option is incorrect because the involvement of the facial nerve (cranial nerve VII) is not a characteristic feature of lateral medullary syndrome.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that lateral medullary syndrome often presents with a combination of cranial nerve and spinal tract signs, which can be ipsilateral or contralateral depending on the affected structure.

**Correct Answer: D.**