Playing with his third NHL club, Lumme remained a prominent member on his team's blueline. With 28-, 40- and 25-point seasons in Phoenix, Lumme finishing second among team defencemen in scoring behind Teppo Numminen in all three campaigns. On June 23, 2001, he was traded from Phoenix to the Dallas Stars in exchange for forward Tyler Bouck. Lumme played 15 games with the club in 2001–02. He left the Stars on October 29, 2001, to briefly visit his family in Finland after receiving permission from general manager Bob Gainey. His wife Minna and two kids had planned to join Lumme in Dallas during the season, but were reluctant to take a plane after the recent 9/11 terrorist attacks. Lumme and coach Ken Hitchcock clashed openly during his brief time in Dallas, however, and he was put on waivers. After clearing, he was traded to the Toronto Maple Leafs in exchange for another veteran blueliner, Dave Manson, on November 21, 2001. The deal was initiated by Maple Leafs general manager Pat Quinn, Lumme's former coach and general manager in Vancouver, who commended Lumme as a "cornerstone" for the Canucks' success during his time with the club.