My nominations:

The Future - Leonard Cohen
song: https://www.youtube.com/watch?v=vnaxvBsyigM
genre: rock
lyrics: http://www.sing365.com/music/lyric.nsf/The-Future-lyrics-Leonard-Cohen/A77873BA639BF30D48256AF0002911C7

Ketzele Baroyges - Barry Sisters
song with lyrics in Yiddish, English and Russian: https://www.youtube.com/watch?v=GtcoSxtCBqo
genre: klezmer

Long Steel Grass (Noche Espagnola) - Edith Sitwell & William Walton
the relevant song is 2:50-5:25 of this video (I couldn't find just the song I was looking for on youtube): https://www.youtube.com/watch?v=Wsfyag25y4o
genre: classical
lyrics: http://www.recmusic.org/lieder/get_text.html?TextId=15091

The Ragpicker's Dream - Mark Knopfler
song with lyrics: https://www.youtube.com/watch?v=FyEJbdPBc6A&index=5&list=PLfd74nN-JPu8EjffqnKmA-R2sdPFhTkew
genre: folk country I guess?

Fistful of Rain - Warren Zevon
song with lyrics: https://www.youtube.com/watch?v=yv-MVz0kYk0
genre: rock