> This might be the work of Annie Brown...

The problem with this is that the opening stanza about the unpaid mason was published by David Herd in 1776 (see Child 93P). That's about seven years before Mrs Brown's first ballad manuscripts were written, and at least 24 years before she gave Robert Jamieson her version of Lambkin (which isn't in any of her surviving manuscripts).

Sigrid Rieuwerts reproduces a letter from Mrs Brown to Jamieson in September 1800, in which she says: "as to the fragment of Lamekin upon reading over the edition of it that is in herds Collection I find that mine differs from it very materially tho the story must certainly have been the same. If you wish to have my way of it I shall send it." (The Ballad Repertoire of Anna Gordon, Mrs Brown of Falkland, p. 47) So it seems clear that she had read Herd's version before she wrote down her own for Jamieson.

(Whether she actually independently knew another version with a similar opening or created her own version influenced what she found in Herd is, of course, another question.)