If we are talking about the late 1800's and early 1900's, I could see the construction of a whole range of small warships uniquely created to wage war in the Great Lakes, both along the coasts and against lake traffic far out "at sea".
By 1917, this might include "lake battleships" - ships between 10,000 and 25,000 tons, similar to traditional predreadnoughts but lacking the intermediate range heavy guns, a powerful anti-aircraft battery for the period,with "modern" protection schemes, and heavy armament gained at the expense of range and endurance. Something more than a coastal monitor, but less than a true ocean-going battleship. Such as:
HMCS Ojibwa
Sister ships HMCS Huron, HMCS Niagra, HMCS St. Andrew
Full-load displacement 22,000 tons
Main armamament - six 13.5 inch guns in two triple turrets one fore, one aft
Secondary battery - twelve 6 inch guns in casemates, six to a side
AA battery - a mix of 3 inch rapid fires and 40mm, 20mm, and .50 cal open mounts
Main belt - 13 inch in "all or nothing" layout
Main gun turrets and barbettes - up to 13 inch
Deck - 2 to 4 inch
Speed - 18 Kts
USS Andrew Jackson
Sister ships USS US Grant, USS Stand Watie
A US attempt to develop a multi purpose ship mainly optimized for attacking Canadian lake traffic and quick raids on Canadian/British coastal facilities. A sort of "mini pocket battleship" without the endurance requirements
Full Load displacement 16,500 Tons
Main armament - three 12 inch guns a single triple turret aft
Secondary battery - 10 5.5 inch in port and starboard casemates.
Main belt - 8 inches
Main turret and barbette -8-10 inches
A flight deck and hangar forward capable of handling 10 Curtiss GN-1 scout bombers.
Speed - 25 kts
The period 1890-1920 would be the heyday of the Lake Commands. With the introduction of effective land-based warplanes, most major combat ships in the Great Lakes would be either scrapped or removed, except for those which could be repurposed as stationary batteries. While the shallow waters would be a problem, small coastal submarines might also be very effective.