I see that your question has been posted for a couple of weeks with no answer. I am a St. Louis native and am not aware of a Lake Sherman anywhere near downtown St. Louis. I also googled "Lake Sherman" and could not find one in Missouri or Illinois. Possibly is it Lake Sherwood or by another name?
There are several small lakes in the outer suburbs of St. Louis, both in Missouri and on the east side of the Mississippi River, in Illinois.