A rap lyrics generation algorithm with deep learning was also recently published [1] in KDD conference and it also got quite a lot of publicity in other media: see the associated website at http://deepbeat.org.
Author of DeepRhyme here. With respect to the authors of DeepBeat, what they are doing is less ambitious. They are taking full existing lines out of a rap lyric corpus and assembling it into a verse that rhymes and makes sense. There is a paper that is very similar to what I did : http://www.emnlp2015.org/proceedings/EMNLP/pdf/EMNLP221.pdf . It's hard to compare our models, because they don't give much output text. They trained on 1% of the data I did, so I'm a bit dubious how successful they could have been.
I am writing a followup post where I'm going to talk about previous work, I hope no one takes any disrespect.
Instead of completely banning actual lines from other material, it might be interesting to allow D-Prime to quote or slightly modify a phrase if it met some high threshold of notability.