Lawsuits Mesothelioma Lawsuits mesothelioma involve victims who have been exposed to asbestos. Veterans, shipyard workers and manufacturers are among the victims. The first step is choosing an attorney who has expertise in mesothelioma lawsuits. A reputable attorney will provide you with a free consultation and assist you in determining your options. Statute of limitations Mesothelioma is a cancer that affects the mesothelium which is a layer of tissue that covers the majority of internal organs. It can affect the testicles, lungs or abdomen.