At the risk of incurring the outrage and Wrath of the Patons, I still think the standard version is one of the dumbest songs ever wrritten. Beautiful tune & Tannahill did other good songs, but this one lacks lots of stuff. Still, other verses have saved it...  

Aside from the well-known "Wild Mounting Time" of the Kippers, I've located some additional verses in some obscure publications:

I walked my dear old collie,
Across the blooming bower,
But she never stopped to piddle,
Though I walked her half an hour.
Will you go, Lassie, go?

                  Steve Suffett

         And we'll all go together,
         As we walk our bloody dogs,
         Regardless of the weather.
         Will you go, Lassie, go?

                   Steve Suffett
 

 I will give my love a pooch
 By yon clear crystal fountain
 And in it he will scootch
 While the hours I am countin'
 
 Will ye go Lassie Go
 Will ye go  in the heather
 If you feed him liquid dog chow
 You won't have to wait forever
 
 Will ye go, Lassie go?

              Frank Hamilton
 

If a Hamburg rat gets worms
He will send for uncle Herman
Whose renowned throughout the land
For de-worming German vermin
Will ye go lassie go.

              Dr. Mark "Gaffer" Ferris (preserved by Jon Freeman)