Stage IV Breast Cancer: This is the most likely diagnosis given the presence of metastasis to the ipsilateral lung. Male breast cancer, although rare, can metastasize similarly to female breast cancer, and lung metastasis is a common site for advanced disease.

Locally Advanced Breast Cancer (Stage III): Although less likely than Stage IV due to the presence of metastasis, locally advanced cancer could potentially involve extensive disease in the chest wall or skin, with a separate primary or metastatic lesion in the lung that is not clearly connected to the breast cancer.
Inflammatory Breast Cancer with Metastasis: This aggressive form of breast cancer can present with rapid progression and metastasis, including to the lungs, and is known for its poor prognosis.

Lung Primary with Metastasis to the Breast: Although rare, it's crucial not to miss a primary lung cancer that has metastasized to the breast. This diagnosis would significantly alter treatment and prognosis.
Lymphoma with Breast and Lung Involvement: Both Hodgkin and non-Hodgkin lymphoma can involve the breast and lungs, presenting similarly to metastatic breast cancer. Missing this diagnosis could lead to inappropriate treatment and poor outcomes.
Metastatic Disease from Another Primary Site: Other cancers, such as prostate, gastrointestinal, or melanoma, can metastasize to both the breast and lungs. Failing to identify the true primary site could result in incorrect treatment.

Sarcomas (e.g., Angiosarcoma) of the Breast with Lung Metastasis: Sarcomas are rare tumors that can occur in the breast and metastasize to the lungs. They have distinct treatment approaches compared to carcinomas.
Phyllodes Tumor of the Breast with Lung Metastasis: Although mostly benign, a small percentage of phyllodes tumors can be malignant and metastasize, including to the lungs.