Alimta is a new cancer drug used to treat malignant pleural mesothelioma. Alimta is given with cisplatin, another anti-cancer medicine. Malignant pleural mesothelioma is a type of cancer that affects the inside lining of the chest cavity. It is usually associated with asbestos exposure.limta is a new cancer drug used to treat malignant pleural mesothelioma. Alimta is given with cisplatin, another anti-cancer medicine. Malignant pleural mesothelioma is a type of cancer that affects the inside lining of the chest cavity. It is usually associated with asbestos exposure.