There is a melody for "Lady Franklin's Lament for her Husband" in the "Oxford Book of Sea Songs" edited by Roy Palmer that is a bit different from the popular version of the ballad. I show it below in ABC notation. I can't do those fancy links for MIDI files but if you send me a Personal Message with an e-mail address I can send a MIDI file that way.

T:Lady Franklin's Lament for her Husband
M:4/4
L:1/8
S:Oxford Book of Sea Songs, ed. Roy Palmer
R:Song
K:D
(D>F)|A2A2 B2 A>F|(E>D) (E>F) D3"'"D|
E2 (E>F) (G>F) (G>A)|B2B2 A2"'" A>A| BBBB d2 c>B|
A2d2 F2"'" (F>E)|D2 AA (B>F) G>E|E2 D2 D2||