Malignant Pleural Mesothelioma: This diagnosis is highly likely due to the pleural-based location and the description of the mass, which is consistent with the typical presentation of mesothelioma. The speculated margins suggest an aggressive nature, which is also characteristic of this malignancy.

Pleural Metastasis: Given the pleural-based location and the lobular, soft tissue appearance with speculated margins, metastasis to the pleura from another primary site (e.g., lung, breast, or ovarian cancer) is a plausible diagnosis. The speculated margins can indicate aggressive behavior, common in metastatic disease.
Solitary Fibrous Tumor of the Pleura: Although less common, solitary fibrous tumors can present as pleural-based masses with varied imaging characteristics, including lobular contours and speculated margins, especially if they are malignant. They are usually well-circumscribed but can have a broad base on the pleura.

Lung Cancer with Pleural Involvement: It is crucial not to miss a primary lung cancer that has invaded the pleura, as this significantly affects staging and treatment. The speculated margins could represent invasion into the pleura or chest wall, indicating a more advanced stage.
Sarcoma (e.g., Pleural Liposarcoma): Although rare, sarcomas can present as pleural-based masses. Missing this diagnosis could lead to inappropriate treatment and a poor prognosis.

Pleural Lymphoma: Primary pleural lymphoma is rare but can present as a pleural-based mass. It might show a variety of imaging features, including lobular contours, though it is less likely to have speculated margins.
Pleural Schwannoma: A benign nerve sheath tumor that can occur in the pleura, presenting as a well-defined mass but occasionally with more aggressive features if malignant. It is much less common than other diagnoses listed here.