Protect Access to Justice for Veterans Act of 2023 This bill limits attorneys' fees for claims involving individuals who were exposed to contaminated water at Camp Lejeune in North Carolina between August 1, 1953, and December 31, 1987. Further, the bill requires an attorney representing an individual for such a claim to disburse the funds from any judgment or award to that individual before collecting any compensation for services rendered. The bill establishes certain penalties for violations.