Each state has its own deadlines, called statutes of limitation. There are strict deadlines for filing lawsuits after becoming aware that you have an asbestos disease or after a loved one dies from an asbestos disease.
Virginia law requires an individual to file a lawsuit within two years of the date "when a diagnosis of asbestosis, mesothelioma or other disabling asbestos-related injury or disease is first communicated to the person or his agent by a physician; however, no such action may be brought more than two years after the death of such person."
Your rights vary depending on many factors such as your residence, where you were exposed to asbestos, and the residence of the responsible asbestos companies. Each state has its own laws and remedies. The time limits applicable to your lawsuit may vary.