Mesothelioma Compensation Many asbestos victims can receive compensation through a range of legal options. Compensation can be used to pay for medical bills and other expenses. A top mesothelioma attorney will analyze your case and explain all types of compensation available. They can also provide an accurate estimate of how long your lawsuit will take. Personal Injury Claims Mesothelioma is an asbestos-related cancer that demands expensive cancer treatments, travel expenses and costs for caregiving, which are not covered by health insurance.