The song quoted by Joan shares lines with "Oh, No, Not I", but the young maid says not to put your trust in the "green willow tree". I had always understood that to be a reference to a folk abortion remedy. There is a reference to willow in this context in The Shipping News, if I remember correctly.
The song is known in Newfoundland, and Stan Rogers did a version, but it must surely be from the UK or Ireland as there are no lords of high degree in Newfoundland. Nature's ladies and gentlemen, yes, but no lords of high degree.:) There are "maids", though, as young girls in Newfoundland are still called that much as they were in western England in the time of Thomas Hardy.
Tree songs -- there is "Lemon Tree". I suppose "The Lumberjack's Alphabet" might qualify, although they list things necessary to cut trees down. You'd think a country like Canada would have lots of songs about trees, but oddly enough none come to mind except in the context of lumberjack and woodsman songs, where they have a tendancy to fall on young men.