Byron's "We'll Go No More A Roving" was set to music by Alexander Lee and published in 1852 by E. H. Wade, Boston. it was sung on tour by the soprano, Emily Coad.
Many others followed with arrangements. See American Memory for Lee's sheet music. I "believe" that this pre-dated English arrangements, but verification is needed. It looks like the one on which Dyer-Bennet based his version.