Going to the Predators in return were defenseman Brett Lebda and forward prospect Robert Slaney, the team said.
The key to the deal was Lombardi, who will be playing for his fourth NHL team in an eight-year career.
The blueliner played only two games for Nashville last season after suffering a concussion, but in 2009-10 with Phoenix, the 29-year-old racked up 19 goals and 53 points in 78 contests.
The 23-year-old Franson, meanwhile, has compiled 14 goals and 50 points in 141 games over his first two NHL seasons with the Predators.
Lebda, who won a Stanley Cup with Detroit in 2008, played in 41 games for the Leafs last season, scoring one goal and four points. He has totaled 19 goals with 72 points in 367 career games.