No person shall drain, lower, or in any manner reduce or divert the water supply of any natural or perennial lake, if the area exceeds twenty acres at low water stage or if the lake is of such depth and character as to have more economic importance for aquaculture, hunting, or other purpose than the bed of such lake would have for agricultural purposes. Any person intending to drain, lower, divert, or in any way reduce the waters or water supply of any natural or perennial lake shall, before commencing the construction of any such work for drainage or diversion, make application to the Department of Natural Resources for a permit to do so.