Final answer:
A drooping of the arch of the soft palate with uvula deviation to the unaffected side is typically due to damage to Cranial Nerve X (Vagus Nerve) or Cranial Nerve IX (Glossopharyngeal Nerve), resulting in asymmetrical motor function of the soft palate muscles.
Step-by-step explanation:
The lesion that leads to a drooping of the arch of the soft palate with the uvula deviating to the unaffected side is a result of a damaged cranial nerve, specifically the Cranial Nerve X (the Vagus Nerve) or possibly the Cranial Nerve IX (the Glossopharyngeal Nerve). These nerves are responsible for the motor function of the soft palate. When there is damage to one side of these nerves, the muscle on the affected side cannot function properly. Hence, when the patient attempts to lift the soft palate, the muscle on the intact side does the lifting, pulling the uvula away from the damaged side. This results in the uvula pointing toward the healthier, functioning side, causing what is known as uvula deviation. This condition can have several underlying causes, such as a brainstem lesion, peripheral nerve damage, or other neurological conditions.