I’m not sure if it applies to Coast Guard vessels, but the Treaty of Ghent, which ended the War of 1812, imposes strict limits on the number of naval vessels that either country can operate on the Great Lakes. If that is the case, they would have a lot of area to cover.
I know the Coast guard on the lakes works pretty closely with their Canadian counterparts. I know they don't worry about borders in the case of rescues. Just whoever is closest.
Just last summer I read about the coast guard responding to a boating accident on the Windsor side of the river. They took injured people to a waiting ambulance at a Canadian dock.