you need an post process material for the fog. you can mask it based on height and other stuff too
i have the nodes that b made in this link that will mask the effect above the water plane, if you use the material in a bound post volume you can limit its size to just the lake.
the post should be enough for you to recreate them, but let me know if you want me to upload it for you.
you will also need to recreate the exponential height fog inside the material