John Lewis Civil Rights Fellowship Act of 2022 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 promote studies, research, and international exchange in the subject of nonviolent civil rights movements around the world. The J. William Fulbright Foreign Scholarship Board shall annually select at least 25 qualified individuals when feasible to serve as fellows in the fellowship program. 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.