Playing the position of defenceman, Norwood was drafted in 1979 by the Quebec Nordiques. He also played for the Washington Capitals, St. Louis Blues, Detroit Red Wings, New Jersey Devils, Hartford Whalers, and Calgary Flames. After his stint with the Flames, he retired from professional play in 1994, only to return to active play a year later in the International Hockey League for two seasons before hanging up the skates for good.
In 503 NHL games, Norwood had 58 goals, 153 assists, and 1,099 penalty minutes. Lee served as the head coach of the Eastern Michigan University hockey team but was released from his position after the 07–08 season. He currently does work on behalf of the Red Wings Alumni Association.