I do not believe that the lake would freeze at the bottom only because of the fact that fish ( sharks mostly) live deep in the waters and it is actually warmer down there. the higher up you are, the more closer you are to the atmosphere and the climate change. Anything way under the water does not always get affect by the climate. the only thing that would affect anything for the most part underwater could be underwater volcanic eruptions and underwater earthquakes, which would essentially cause the bottom of the ocean or lake to split and become reefs.