Mesothelioma Lawyers Choosing the right mesothelioma lawyer will help you file your asbestos lawsuit as simple as is possible. A competent attorney can assist you at every stage of the process from creating legal documents to pursuing the highest amount of compensation. A good law office will provide a no-cost case evaluation. They usually work on a contingent basis. Statute of Limitations Mesothelioma patients have a limited window to file a lawsuit against asbestos. If they don't submit their claims before the statute of limitation runs out