Mesothelioma Lawsuits People who suffer from asbestos-related illnesses like mesothelioma can seek compensation from companies responsible for their exposure. Compensation can cover medical costs and lost wages. Most lawsuits follow a similar legal process, despite the fact that each case is different. An experienced mesothelioma attorney can handle all legal process so that patients and their families can concentrate on the treatment. Statute of limitations Mesothelioma victims must file their claims within certain deadlines set by state law