Don't mind me. 

So I just realised something, The Ballad of Jane Doe is actually a lament and Noel's Lament is actually a ballad. The titles are a reflection of what the songs want to be not what they actually are. The Ballad of Jane Doe isn't a ballad because Jane doesn't have a story, rather she is mourning the loss of who she was before her death and her loss of identity, thus making it a lament. She wants to be singing an actual ballad, she's wishing for a story and closure on who she was but it's not possible since she has no story to tell. In Noel's case his song isn't a lament because he isn't mourning anything, he's telling the tragic story of this hooker he wishes he could be. At the end of Monique's story she dies, Noel is wishing for someone to mourn him. He wishes he was Monique not only for the 'thrill' of her life compared to his own but also for the tragedy and loss that comes with it because he wants to be mourned and to have a grander legacy than the seemingly dead-end life he had before, but because he's telling us the story of Monique, his song is a ballad.