James Dick didn't verify the source. The note from James C. Dick, The Songs of Robert Burns (1903; rpt. Folklore Associates, 1962, p. 488; s.v. No. 334. O, Lady Mary Ann looks o'er the castle wa') is: "The tune was printed for the first time in the [Scots Musical] Museum. A tune entitled Long a growing is said to be in Guthrie's MS. of the seventeenth century" [underline added].