Mr. Sundae opened this place by the lake

Dana is confused…

I snapped this picture on our local lake. So, I’m confused. Does this mean someone named Sundae is by the lake? Or that ice cream sundaes are by the lake and if that’s the case it should be named “Sundaes are by the Lake?” Or is it possible they were trying to make a pun on “Sundays by the lake” except they humorously changed Sunday to Sundae?