Camp Lejeune Justice Act of 2020 This bill allows certain individuals to sue and recover damages for harm from exposure to contaminated water at Camp Lejeune in North Carolina between August 1, 1953, and December 31, 1987. This action is available only to individuals who were exposed to contaminated water for at least 30 days. The bill prohibits the U.S. government from asserting immunity from litigation in response to such a lawsuit. The bill also prohibits an individual who brings such an action from bringing a separate tort action against the United States based on the same harm. However, an individual who had previously sued based on such harms, regardless of the reason for the termination of the earlier lawsuit, may sue under this bill.