(1) From William Stenhouse's note to the song "Lord Gregory" (The Scots Musical Museum, vol. 2, 1853 edition; rpt. Folklore Associates, 1962, p. 3):

This is a very ancient Gallowegian melody. The two verses adapted to the air in this collcction [sic], were compiled from the fine old ballad, entitled, "The Lass of Lochroyan," which was first published in a perfect state by Sir Walter Scott in his Minstrelsy of the Border, vol. ii. p. 411. Burns remarks, that "it is somewhat singular, that in Lanark, Renfrew, Ayr, Wigton, Kirkcudbright, and Dumfries-shires, there is scarcely an old song or tune, which, from the title, &c. can be guessed to belong to, or be the production of these counties.. This, I conjecture, is one of these very few, as the ballad, which is a long one, is called, both by tradition and in printed collections, 'The Lass o' Lochroyan,' which I take to be Lochroyan, in Galloway."--Reliques, p. 196.

(2) From James C. Dick, The Songs of Robert Burns (1903; rpt Folklore Associates, 1962, p. 398):

No. 138. O mirk, mirk is this midnight hour. Thomson's Scotish Airs [sic], 1798, 38. 'Written for this work by Robert Burns. Air, Lord Gregory.' Among the Dalhousie MS. in Brechin Castle. The tragic ballad of Lord Gregory, containing about sixty stanzas, better known as Fair Annie of Lochryan, is the foundation of Burns's verses. The earliest printed fragment is in Herd's Scottish Songs, 1776, i, 149, entitled The bonny lass o' Lochryan. Two double stanzas, with the tune, were engraved in the Scots Musical Museum, 1787, No. 5. This was one of the few historical ballads which made an impression on Burns. Thomson had informed him that Dr. Wolcot had written a song on the subject, and he replied on January 26, 1793, by enclosing a copy of the verses in the text. A few weeks before his death, Burns touched up the song, and sent a copy to his friend Alex. Cunningham.
The tune is not in print before the Scots Musical Museum, 1787, No. 5. According to Stenhouse, it is an old Gallowegian melody. The music is also in Urbani's Scots Songs, 1792, 1; and Dale's Scotch Songs, 1794, iii, 119.

~Masato