Greene attended St. Paul's School in Brooklandville, Maryland, where he was a four-year letterwinner on the varsity lacrosse team.
[3] After the 1943 season, Ray reported for military service in the Navy and when the war ended, he resumed his lacrosse career at Johns Hopkins University.
Ray was credited by Bob Scott in his book, Lacrosse: Technique and Tradition, with scoring the winning goal in the 1948 Navy game.
Greene spent two years coaching at his prep alma mater, St. Paul's School, where he led the team to 10–2 and 9–1 records in 1949 and 1950, respectively.
[6] Greene is among 18 players or coaches from St. Paul's in the National Lacrosse Hall of Fame, including Jim Adams, Scott Bacigalupo, Jeff Cook, Howdy Myers, and Don Zimmerman.