**Core Concept**
The underlying principle being tested is the use of immunohistochemical markers in the diagnosis of undifferentiated tumors, particularly in the context of lung cancer. **Immunohistochemistry** is a crucial tool for identifying specific proteins or markers on tumor cells, helping to narrow down the diagnosis. In lung cancer, especially in small cell lung cancer, certain markers are more commonly expressed.

**Why the Correct Answer is Right**
Given the clinical presentation of haemoptysis and cough in a smoker, along with the finding of an undifferentiated tumor on bronchoscopic biopsy, the most helpful immunohistochemical marker would be one that is specific for neuroendocrine tumors, such as **synaptophysin** or **chromogranin**, but most specifically for small cell lung cancer, **TTF-1 (Thyroid Transcription Factor 1)** is highly relevant as it is often positive in small cell lung carcinoma.

**Why Each Wrong Option is Incorrect**
**Option A:** Without the specific details of option A, it's challenging to provide a precise reason for its incorrectness, but if it's not related to neuroendocrine or lung-specific markers, it would be less relevant.
**Option B:** Similarly, without specifics, if this option does not relate to markers commonly found in lung tumors, especially those with neuroendocrine features, it would not be the best choice.
**Option C:** If this option is not a marker associated with lung cancer or neuroendocrine tumors, it would be incorrect.
**Option D:** Assuming this is not a relevant marker for lung cancer diagnosis, it would be an inappropriate choice.

**Clinical Pearl / High-Yield Fact**
In the diagnosis of lung cancers, particularly those that are undifferentiated, **TTF-1** is a critical marker because it is positive in the majority of small cell lung cancers and many non-small cell lung cancers, especially adenocarcinomas. This can help guide further treatment and management.

**Correct Answer:** D. TTF-1