This song was widely popular, and turns up as The Cruel Father and Affectionate Lover, The Imprisoned Lady, The Daughter in a Dungeon, Love Laughs at Locksmiths and so on.  It's been found in England, Ireland and Canada.  As a result, there is more than one tune known for it.  I haven't heard of the band you mention; did they say anything about their sources?  No way of guessing at the tune until we know that.

As Nutty just mentioned, there's a set from Nova Scotia, with tune, in the DT: SINCE LOVE CAN ENTER AN IRON DOOR

There are a number of broadsides at  Bodleian Library Broadside Ballads,  titled variously Mary Ann and her Servant Man and The cruel father and affectionate lovers.

So far as identifying an "original" tune goes, that may well be impossible; unless the song can be traced to a presumed first appearance in print with tune.  If Bruce Olson doesn't have the information (I don't have time to check his site just now) then probably nobody has.

Just by way of a footnote, it's helpful if you can use the standard format when posting lyrics; makes it easier if they are eventually incorporated into the Digital Tradition database: full details are in the FAQ thread at the top of the main Forum page.  It's also helpful if you add any background information you may have, such as sleevenotes and recording details if you've taken the text from a record; both for other people in the future, and to aid searching now.

Malcolm