You're welcome here, and we always value such contributions.  I couldn't get hold of a copy of Mary Barton today, but your reference to Lloyd's book (I have a different edition, so the page numbers you gave don't work for me) does make me wonder if you might possibly be thinking of Jone O' Grinfelt /Greenfield (which is sometimes called The Four-Loom Weaver, and occasionally The handloom Weaver's Lament), but which is actually a completely different song.  The description of the melody might suggest that.  Could you possibly quote a few lines from Mrs. Gaskell, if she gave any?

Malcolm