Top Mesothelioma Lawyers A diagnosis of mesothelioma is extremely stressful for patients and their family members. This process can be made easier by selecting a law firm with experienced mesothelioma lawyers. The top mesothelioma law firms are familiar with the statutes of limitations for each state, and may make a claim before they expire. can also pursue compensation for victims through a verdict or settlement. Weitz Luxenberg Weitz Luxenberg, a law firm in New York City, has been helping mesothelioma victims for over 30 years.