It would be an odd place for ships to engage in combat but massive cities on both sides are on or within a few miles of the water, and protecting those with a fleet of any size would be important if conflict were to occur. Do we know if the U.S. or Canada has made diagrams, done exercises, etc. of such a situation?
Has it already happened?
It has already happened. In the war of 1812 the conflict centered around the Canadian border, and after the British had made large gains on the US such as taking Detroit, the US needed to secure the lakes. This happened in the Battle of Lake Erie, in which Commodore Oliver Hazard Perry defeated the British, allowing the US to push back the British, defeat the native Americans, and counter-invade Canada.
The War of 1812 involved a number of naval engagements throughout the Great Lakes. Control of the Lakes was essential to both sides, as it was naval forces that provided the logistical component of the campaign. This resulted in a naval arms race between the Americans and British.
The British held the initial advantage against the Americans, as they already had a few fresh water ships in their possession (the Canadas operated a quasi-naval force known as the Provincial Marines). The onset of war the Provincial Marines operated two sloops-of-war, and two brigs in Lake Ontario (in addition to two schooners also requisitioned at the onset of war). They also had two ships in Lake Erie (bolstered to three with the completion of the HMS Lady Prevost weeks after the war declaration).
Contrasting this, the US naval presence was a single brig in Lake Ontario, and another one being serviced in Lake Erie. They were also reinforced by requisitioned ships converted to gunboats. The Provincial Marines made efforts to seize both ships, capturing the USS Adams during the siege of Detroit (attempts against the Lake Ontario-based USS Oneadia were rebuffed). With the capture of Detroit, naval supremacy of Lake Erie was originally held by the British.
The advantage in Lake Erie was negated not to long after, as the Americans engaged in massive shipbuilding projects along the lake. By 1813 the Royal Navy was restricted to largely blockading actions. Lack of support from Captain James Yeo (commander of the entire Great Lakes squadron, though he was primarily interested with Lake Ontario), as well of quality of ships led to the Royal Navy's Erie Squadron to be defeated.
The defeat of the British Erie Squadron granted the Americans uncontested supremacy west of Lake Ontario, and seriously bolstered its Squadron in Lake Ontario. It also provided the space the Americans needed to send several ships to Lake Huron. However, as opposed to any naval engagements, these ships were sent to displace the British forces that seized American forts at the beginning of the war (they would actually fail in dislodging the British from these forts though).
As for Lake Ontario, only a few skirmishes broke out, with the composition of the both sides matching the other for the latter half of the war. Both commanders (Yeo and Commodore Issac Chauncey) were afraid of losing the initiative, so they largely refrained from entering a decisive engagement. In particular, Kingston was the gate keeper to the St. Lawrence River (and the more populated Lower Canada). The Royal Navy's primary goal in Lake Ontario was to defend Kingston.
By the wars end, the resulting arms race produced the only first-rate ship of the line to see service in freshwater, the HMS St. Lawrence. The ship acted somewhat as a fleet in being, tipping the balance in Lake Ontario for the British, as the Americans Squadron was unwilling to set sail to engage her. There was five more ship-of-the-liness undergoing construction by the wars end (two American, three British) .
The War of 1812 ended with a treaty calling for the general disarmament of the Great Lakes (each side was technically permitted to have one small warship for policing). While some of the ships were broken up, many of the ships saw some form of service as late as the 1820s and 1830s.
It's not that odd of a place for naval combat; these lakes are still hundreds of miles long, have a combined surface area of a little less than the Black Sea, and navigation is possible between them via rivers and canals. And as /u/Edsman1 has said, the battle for control over the lakes was a very big deal in the War of 1812.
People are forgetting the naval warfare conducted during the Revolution as well. The American invasion of Canada couldn't have gone forward without naval operations. The British invasion that culminated at Saratoga was likewise begun with extensive naval operations.
Anyone interested in the history of naval operations during the conflict, on the sea as well as the lakes and rivers, needs to pick up Sam Willis' The Struggle for Sea Power. It provides a fresh perspective on the war.