**Core Concept**
The patient's presentation of malena (black, tarry stools) and pigmented lesions on the mouth and lips, along with a family history, suggests a diagnosis related to a genetic disorder affecting melanin production.

**Why the Correct Answer is Right**
The patient's symptoms and family history are indicative of Peutz-Jeghers syndrome (PJS), a rare genetic disorder characterized by the development of benign hamartomatous polyps in the gastrointestinal tract, along with mucocutaneous melanin deposits. The polyps can cause gastrointestinal bleeding, leading to malena, while the melanin deposits result in characteristic blue or dark brown macules on the skin and mucous membranes. The genetic basis of PJS involves mutations in the STK11 (also known as LKB1) gene, which encodes a tumor suppressor protein involved in cell growth and division.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is not relevant to the patient's presentation of malena and pigmented lesions.
**Option B:** While gastrointestinal bleeding can be a symptom of Peutz-Jeghers syndrome, this option does not account for the pigmented lesions.
**Option C:** This option does not address the patient's family history or the specific combination of symptoms and signs.

**Clinical Pearl / High-Yield Fact**
Peutz-Jeghers syndrome is an autosomal dominant disorder, meaning that only one mutated copy of the STK11 gene is required to cause the condition. This has significant implications for genetic counseling and the risk of transmission to offspring.

**Correct Answer: C. Peutz-Jeghers syndrome.**