Mesothelioma Lawsuit Settlement Amounts Many asbestos companies have ignored the risks of Mesothelioma over years, putting profits ahead of people's lives. Asbestos victims can file a mesothelioma lawsuit to claim compensation. Trust funds, veterans benefits and settlements are all available to help mesothelioma sufferers. A mesothelioma attorney can assist you in determining the best compensation source for your case. What is of an average Settlement? Settlement amounts vary significantly. The settlement amount varies depending on the case.