Small Cell Lung Cancer (SCLC): Given the presence of a lung mass and metastasis to the liver, SCLC is a strong consideration. It is a type of neuroendocrine tumor known for its aggressive behavior and early metastasis. The fact that it originates in the lung aligns with the provided clinical scenario.

Typical and Atypical Carcinoids: These are neuroendocrine tumors that can arise from the lung or thymus and have the potential to metastasize to the liver. They are less aggressive than SCLC but can still cause significant morbidity.
Medullary Thyroid Carcinoma: Originating from the thyroid, this cancer can metastasize to the liver and lungs. It is a neuroendocrine tumor and can present with a variety of symptoms depending on the location and extent of metastasis.
Thymic Neuroendocrine Tumors: These are rare tumors originating from the thymus and can range from well-differentiated to poorly differentiated (which would be more aggressive). They can metastasize to the liver and lungs.

Pheochromocytoma: Although less likely, pheochromocytoma (especially if malignant) can metastasize to the liver and lungs. It is crucial to consider this diagnosis due to its potential for causing severe hypertension and other systemic effects.
Gastrointestinal Neuroendocrine Tumors (e.g., Pancreatic Neuroendocrine Tumors): While the primary sites mentioned are lung, thymus, or thyroid, it's essential not to overlook the possibility of a gastrointestinal or pancreatic neuroendocrine tumor, which can also metastasize to the liver and lungs.

Merkel Cell Carcinoma: A rare and aggressive skin cancer that can metastasize widely, including to the liver and lungs. It has neuroendocrine features and can be associated with a poor prognosis.
Paraganglioma: Similar to pheochromocytoma but typically found in extra-adrenal sites, paragangliomas can be malignant and metastasize to various locations, including the liver and lungs.