Mesothelioma Lawyers The right mesothelioma attorney will help you file your asbestos lawsuit as simple as it is possible. A qualified attorney will be able to assist you in every step of the process from preparing legal papers to fighting for maximum compensation. A good law office will provide a no-cost case evaluation. They typically work on a contingent basis. Statute of Limitations Mesothelioma patients have a finite time to bring a lawsuit against asbestos companies. They must file their claims before the statute of limitations expires