Some previous discussion on "Our Captain" may be found in the thread on "Fighting for Strangers" (a version of which Joe posted above):
http://mudcat.org/thread.cfm?threadid=31423
Perhaps some Mudelf will add this link to the "Related threads" section above.

pavane quoted two other verses from "The Maidens Lamentation" which resembled those in "Our Captain", aside from the one quoted above. One began "Alas my dearest joy, why wilt thou leave me" and the other "Why wilt thou cross the seas to fight with strangers". A fuller title for the cited tune was also given: "I am so deep in love or Cupid's Courtesie".

Somewhere, Malcolm Douglas provided an ABC of the familiar "Monk's Gate" tune as originally collected by Ralph Vaughan Williams from Mrs. Verrall, singing a shortened "Our Captain" version; RVW later modified the tune to fit it to Bunyan's poem "To Be a Pilgrim", aka. "He Who Would Valiant Be". I'm pretty sure I ran across scans of RVW's notebook entries for Mrs. Verrall's version at the EFDSS Take Six site.

What I haven't tripped across yet are two other tunes this song has been collected with, namely, the one Cecil Sharp collected from Mrs. Overd (Langport, Somerset, 1904) and the one collected from Mrs. Elizabeth Smitherd (Tewkesbury, Gloucestershire, 1908). I also haven't seen a tune or score pointer for "Cupid's Courtesie", although this was apparently a well-known tune. Can someone provide ABCs, send Joe Offer a MIDI, or PM me to arrange sending me scans to ABCify? And who collected the Smitherd tune?