Lack, 29, was 8-7-3 with a 2.64 goals-against average and .902 save percentage in 20 games (18 starts) in his second season with Carolina as the backup to Cam Ward. The Hurricanes acquired goalie Scott Darling in a trade with the Chicago Blackhawks on April 28, and he signed a four-year, $16.6 million contract May 5.
Lack likely will back up Mike Smith, who was acquired by Calgary in a trade with the Arizona Coyotes on June 17. Brian Elliott and Chad Johnson were the Flames goaltenders last season.
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Lack had two concussions last season and was publicly criticized during a rough stretch of play by Hurricanes coach Bill Peters.
"He's had his ups and downs in Carolina," Treliving said. "We're looking forward to getting him in with our guys, with (goaltending coach) Jordan Sigalet, and working with him.
"He's an extremely hard worker. He's really dedicated to his craft … and a really good teammate. We're happy to have him."
Murphy, 24, had two assists in 27 games this season and 37 points (six goals, 31 assists) in 151 NHL games, all with Carolina, who selected him No. 12 in the 2011 NHL Draft. The Hurricanes acquired defenseman Trevor van Riemsdyk in a trade with the Vegas Golden Knights on June 22, one day after he was selected from the Blackhawks in the NHL Expansion Draft.
Kanzig, 22, is 6-foot-7, 247 pounds. He has not played in the NHL after being the No. 67 pick in the 2013 draft. He made his professional debut this season, playing three games for Stockton in the American Hockey League.
Carolina receives a seventh-round pick in 2019, with Calgary getting a sixth-round selection.
Lack, who played two seasons for the Vancouver Canucks, is 54-51-18 with a 2.56 GAA and .911 save percentage in 136 NHL games (121 starts).
The Hurricanes agreed to retain half of Lack's $2.75 million salary for 2017-18.
