You can still file a claim. Medically, there are many studies that show cigarette smoking has nothing to do with the cause of mesothelioma cancer, which is almost exclusively related to having prior asbestos exposure in your work career or during your lifetime.
Regarding lung cancer, cigarette smoking is a known cause of lung cancer, but asbestos is also a carcinogen and also a known cause of lung cancer. Many medical studies showed that workers who were significant smokers, and who also had asbestos exposure, had a 50 to 80 fold relative risk increase over non-smoking/non-asbestos workers, in contracting lung cancer. This is called “synergy” and makes the risk of lung cancer extremely great for smokers who breathed asbestos, and most had no idea that their risk of lung cancer was so vastly increased because of the mix between smoking and asbestos fibers.