Ten players on Tampa Bay's roster, including rookie center Cory Conacher, who has nine goals and 23 points, played for Syracuse this season.
Dan Lacroix and Steve Thomas will handle coaching duties when the Lightning host the Buffalo Sabres on Tuesday night. The pair will then remain as assistant coaches for Cooper.
Syracuse assistant Rob Zettler will take over for Cooper in the minors. Lightning assistant coach Martin Raymond will join Zettler's staff.
Raymond and Lacroix coached Tampa Bay on Sunday in Winnipeg when the Lightning lost 3-2 to the Jets.
Tampa Bay entered this season with playoff aspirations after adding goalie Anders Lindback and defensemen Sami Salo and Matt Carle. Lindback and captain Vincent Lecavalier have been among the players sidelined by injuries.