In August 1988, Lumme signed a two-year contract with the Canadiens. Playing his first season in North America, Lumme split the 1988–89 campaign between Montreal and their minor league affiliate, the Sherbrooke Canadiens of the American Hockey League (AHL). He became the first Finnish player to compete for the Canadiens in team history. While playing in an NHL game against the Detroit Red Wings on December 5, 1988, he suffered a knee injury, sidelining him for some time. He finished the season with 15 points over 26 AHL games, while registering 4 points over 21 NHL games within the Canadiens organization. The following season, Lumme earned a full-time NHL roster spot with the Canadiens.