Seems to me that glaciers would have pushed debris into the lake despite the fact they didn’t scour the bottom.
That’s right, unless the crater was blown right through the ice and the lip was too substantial for the ice to climb over so it flowed around instead.
I agree that the glaciers would seem to have covered the lake as they advanced and retreated, but this is a crater lake (it looks like it is raised above the nearby topography by the crater walls and what’s leftover of the rim) so perhaps the ice wasn’t deep enough here to cover the top of the walls.
The other glacier lakes are scraped out of the flat surrounding rock by the glacier itself, so later glacier advances are going to re-fill the same recess.