Bruce has Lady Casslilles Lilt (Johnny Faa/Jonny Faa, the Gypsiey Laddie) as being in the Skene Manuscripts which dates to the 17th century (correct me if I'm wrong!). (Lady Casslilles being the one that ran away). According to Child the first documented printing was in Tea Table Miscellany (1740).

Scots Musical Museum (last volume published 1803) only says "neighboring tradition strongly vouches for the truth of the story," but says nothing about the melody. The words in SMM are not too dissimilar from Sharp - for example:

"Yestreen I lay in a weel-made bed,
And my good lord beside me;
This night I'll ly in a tenant's barn,
Whatever shall betide me.

"Gae saddle me my black, black steed,
gae saddle an mak him ready.."