(Lady Barnard), left alone at home by her lord, convinces (Little Musgrave) to sleep with her. Her husband returns unlooked-for, and finds Musgrave in bed with his wife. Lord Barnard slays Musgrave in a duel, and then kills his wife
A fragment of this ballad is found in John Fletcher and Francis Beaumont's 1611 play "The Knight of the Burning Pestle," Act V, scene ii:
And some they whistled, and some they sung,
"Hey, down, down!"
And some did loudly say,
Ever as the Lord Barnet's horn blew,
"Away, Musgrave, away!"
There is a somewhat interesting twist in several of the versions. Usually the song says that the wife loves Musgrave/Mattie more than her Lord and all his kin -- but in both of Scarborough's texts and in Creighton and Barry/Eckstorm/Smythe p. 164 and a version from Sharp (Bronson's #42) and another from Karpeles (Bronson's #56) she loves his finger, and in Creighton/Senior #1 his tongue. Maybe it just strengthens the comparison -- but they're interesting body parts to care for; maybe there was more going on in that bedroom than we thought.
It also occurs to me that there is a certain similarity in this tale to "Sir Gawain and the Green Knight." Not in plot, really, but in incident. Note that Lord Barnard kills Little Musgrave in a formal contest in which Musgrave is granted the first blow. This is obviously a variant on the Beheading Game of "Sir Gawain" -- though in fact the contest is older; the first instance of the Beheading Game appears to have been the Irish prose saga of "Fled Bricrend," "Bricriu's Feast" (cf. J. R. R. Tolkien and E. V. Gordon, _Sir Gawain and the Green Knight_, second edition revised and edited by Norman Davis, Oxford, 1967, p. xv); in this, Cuchulainn twice wins the Beheading Game. But Sir Gawain adds to this the temptation of Gawain by a lady while her husband is out hunting. One might say that "Little Musgrave and Lady Barnard" is "Sir Gawain" if Gawain had given in to temptation.
Not that there is much likelihood of literary dependence; "Sir Gawain" was effectively lost (only one copy is extant), and the tale seems to come from a region not associated with the main versions of "Little Musgrave." But there are a number of romances (listed in Tolkien/Gordon/Davis, pp. xvi-xvii) which are similar to "Sir Gawain" though weaker. Most of these are French, but they might have inspired the story.
Of course, there is an important footnote here: Three people ended up in Lord Barnard's bedroom: Barnard, his wife, and Musgrave. Only Barnard came out alive. Thus every detail must have been attested by Barnard. We could not know if there was actually a contest of blows, or what Lady Barnard said; it's perfectly possible, e.g., that Barnard struck Musgrave without warning, and that Musgrave inflicted Barnard's wound after he was himself struck. Or -- well, I leave the rest as an exercise for the reader, until someone comes up with an actual incident that might be the basis for the song. - RBW