Now I remember what else Lord Randal reminded me of.
I riden så by Gjallarhorn. I have no idea how old this particular song is, though--it could be pretty modern. But it's got a similar theme, even though here it's a father and his daughter in a linden grove. She gives birth to two boys under the linden trees and all of them die. But she does give a spoken will, the same way Randal does as he's dying. How the kids die is a bit ambiguous, as it's only described in mythological terms, so I guess they might die as grown-ups by drowning and in battle or something (if anyone knows better, I'd love to know).