**Core Concept**
The patient's presentation of polyuria, polydipsia, nausea, and altered sensorium in the context of a history of lung cancer and a narrowed QT interval on ECG is suggestive of a paraneoplastic syndrome, specifically ectopic hormone production. The narrowed QT interval is a key clue, as it is often associated with hypercalcemia.

**Why the Correct Answer is Right**
The narrowed QT interval on ECG is a classic electrocardiographic finding in hypercalcemia. The patient's symptoms of polyuria, polydipsia, and altered sensorium are also consistent with hypercalcemia, which can cause nephrogenic diabetes insipidus and encephalopathy. The most likely cause of hypercalcemia in this patient is ectopic parathyroid hormone-related protein (PTHrP) production by the squamous cell carcinoma of the lung, leading to a paraneoplastic syndrome.

**Why Each Wrong Option is Incorrect**
* **Option A:** Hypokalemia is not directly related to the narrowed QT interval or the patient's symptoms.
* **Option B:** Hypernatremia is not the most likely metabolic abnormality in this case, as the patient's symptoms are more consistent with hypercalcemia.
* **Option D:** Hypomagnesemia can contribute to hypercalcemia by reducing the excretion of calcium in the kidneys, but it is not the most direct cause of the patient's symptoms.

**Clinical Pearl / High-Yield Fact**
Paraneoplastic syndromes, such as ectopic hormone production, are a common cause of metabolic disturbances in patients with cancer. A narrowed QT interval on ECG is a key clue to the diagnosis of hypercalcemia, which should prompt further investigation for an underlying paraneoplastic syndrome.

**Correct Answer:** C. Hypercalcemia