John Lewis Civil Rights Fellowship Act of 2023 This bill establishes the John Lewis Civil Rights Fellowship Program within the J. William Fulbright Educational Exchange Program (commonly referred to as the Fulbright Program). The fellowship program shall honor the legacy of Representative John Lewis and advance U.S. foreign policy priorities by promoting studies, research, and international exchange in the subject of nonviolent civil rights movements around the world. The Fulbright Foreign Scholarship Board shall annually select qualified individuals to serve as fellows in the fellowship program. The Bureau of Educational and Cultural Affairs may determine the number of fellows for each year, with at least 25 fellows each year whenever feasible. Each fellow shall (1) work in an internship or research position with an approved organization in a country with an operational Fulbright U.S. Student Program, and (2) receive an award sufficient to cover the fellow's reasonable costs during the fellowship period and certain travel and lodging expenses related to the program.