If this is true ("only b/c of melting ice sheet; will dissipate in next few thousand years") then wouldn't we expect water levels to be continuously dropping? Seems more likely that they exist because rain/meltwater makes its way to the basin and keeps them filled (irrespective of whether or not they were originally filled with meltwater from the ice sheet 15kya).
I believe a lot of it is ultimately fed by hundreds of thousands of square kilometers of smaller lakes upstream. The Canadian Shield is dotted with gazillions of lakes, it's crazy to fly over it. And I think it's safe to assume most of those lakes are glacial remnant water, not sure if they're fully refreshed by rain and snow.