It’s certainly possible to have an inch or two of water sitting on top of the ice, but any more than that and it will usually find a way to pass through. The water will flow down through cracks and melt a drain hole, or will flow along the border between the lake and the land.
Try it yourself: get a cup that’s wider at the top than at the bottom, put some water at the bottom of the cup, freeze it, and then put more water on top. Unless the ice is very thoroughly stuck to the cup, it’ll bob upward as water flows around it and displaces it.
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