By the lake - on the shores of the lake

"A house by the lake."
"A house on the shores of the lake."
"A house by the shores of the lake." (does this work at all? Perhaps 'by' already indicates that the location is right next to
the lake. Therefore to say 'by the shores of the lake' is like saying that the house
isn't really right next to the lake, it's only right next to the shore and hence further
away from the water than simply 'by the lake' would mean.)

Are there any subtle differences between these sentences in terms of the idea of the location of the house they seek to convey?

Thanks
Joe.