Maybe Susanne and Garry won't see this now - but here is the answer to their questions perhaps, at this link:

https://mainlynorfolk.info/martin.carthy/songs/theharesdream.html

It says:

The Hare's Dream is printed in Gale Huntington's Songs of the People, a collection of Ulster folk songs from the Sam Henry Collection.

Martin Carthy sang The Hare's Dream in a radio broadcast that was available, undocumented, from Napster before its decline in early 2001. He never recorded it for an official album though.

Len Graham sang The Hare's Lament in 1979 on Joe Holmes' and his Topic album of traditional songs, ballads and lilts from the North of Ireland, After Dawning.