Good Lord, what's the problem? "Tomorrow" is a hell of a lot better in the songs than "he died the next day." Good English it ain't, but it sounds OK. Tomorrow has a nice round sound to it.
Or, let's go whole hog and edit 57 (in Bronson)
Lady Nancy she died as it might be today (let's substitute "as the case may be," or "as it happens")
Lord Lovel he died tomorrow (substitute "on the very next day" or on the following day"), "On the morrow" would be better and would still permit the rhyme with sorrow.
Lady Nancy, she died of pure, pure grief,
Lord Lovel he died of sorrow, -row, -row, (change to unalloyed sorrow- the -row stuff is kitchy)
Lord Lovell he died of sorrow (too much sorrow here- substitute "He had no time to borrow." (doesn't make much sense but avoids repeating "sorrow."

These are old folk songs, full of old constructs, old dialect, sung by the common people, and have not been polished to perfection for inclusion in The Oxford Book of Child Verses for the Sophisticated Semioticist.