WDFW publishes firearms restriction areas by county, I would start there. Google Earth or Maps will show whether there are houses or other buildings that would restrict where you could shoot. Next step would be to ensure there is public access to the lake to either launch a boat or access the shore. Once I did all of that, the local warden would be a good place to try.
If you go out there Saturday morning, you will likely see what lakes are currently hunted.
Finally, Googling the lake's name and words like waterfowl, hunting or the like could turn up additional information.
