I don't really understand Swedish, so I can't tell for sure if a source is named for the above; nothing specific, though, I think. I've removed the accompaniment from the midi in order to make the tune more clear:

Sven i Rosengård (1) midi

A text almost identical to the second one quoted by Masato above is given at Skjaldeners Bibliotek:

Sven i rosengård

Staff notation is provided; similar to the midi already mentioned, but phrased a little differently and worth quoting also:

Sven i Rosengård (2) midi

Thanks to Masato for finding references; I hadn't expected the material to be available. The trick, as it turns out, is to search for Sven i Rosengård rather than Sven i Rosengard.

I have a vague feeling that I've heard a rather similar melody used for a French Canadian analogue of Lord Randal, but I could easily be wrong about that. I will have to check when I unpack the relevant tape.