Conroy, making US$2.4 million this season and under for the same amount in 2007-08, was an integral part of the 2003-04 Flames team that reached the Stanley Cup final.
The 36-year-old hasn't been the same player so far this campaign, struggling with just five goals and 11 assists in 52 games. But he'll join a deeper Flames squad and should help them develop a stronger second line that would ease the load on the top unit centred by Daymond Langkow once injured captain Jarome Iginla returns to the lineup.
In 237 regular-season games with the Flames from 2001-04, he recorded 188 points (60 goals, 128 assists) and put up six goals and 11 assists during Calgary's 2004 playoff run.
He had been on the trading block for weeks before Flames general manager Darryl Sutter decided to pull the trigger.
Lundmark, 26, has four assists in 39 games this season.
The Kings also get a fourth-round draft choice in 2007 and a second-round pick in 2008 in the deal.
Conroy and Lundmark won't have to wait long before meeting their former teammates. The Flames and Kings meet Tuesday in Calgary.