The Crown has asked that Travis Baumgartner be sent to prison with no chance at parole for at least 40 years.
Justice officials say it would be the first use of a federal law passed in 2011 that allows consecutive parole terms to be set in multiple murders.
Baumgartner, who is 22, pleaded guilty earlier this week to one count of first-degree murder, two counts of second-degree murder and a charge of attempted murder.
He shot his fellow guards from a security company while the crew was on a routine night shift reloading ATMs at the University of Alberta in June 2012.
Court has heard that Baumgartner was in debt after buying a new truck, owed friends money and had fought with his mother about paying rent.