Jones is currently on trial in Waterbury, Connecticut, about 20 miles from Newtown, where the shooting took place.
After a civil trial related to damages last month, a Texas jury ordered Jones to pay nearly $50 million in damages to Lewis and Heslin.
Under Texas law, punitive damages can be up to twice the amount of economic compensatory damages but limited to $750,000 per plaintiff.
Midway through that trial, Jones also filed for bankruptcy on behalf of his company, Free Speech Systems.
Prior to his Connecticut trial, Jones’ lawyer tried to transfer the case to a federal bankruptcy court, which the court denied, allowing it to proceed in state court.