Music genre classification, especially using lyrics alone, remains a challenging topic in Music Information Retrieval. In this study we apply recurrent neural network models to classify a large dataset of intact song lyrics. As lyrics exhibit a hierarchical layer structure - in which words combine to form lines, lines form segments, and segments form a complete song - we adapt a hierarchical attention network (HAN) to exploit these layers and in addition learn the importance of the words, lines, and segments. We test the model over a 117-genre dataset and a reduced 20-genre dataset. Experimental results show that the HAN outperforms both non-neural models and simpler neural models, whilst also classifying over a higher number of genres than previous research. Through the learning process we can also visualise which words or lines in a song the model believes are important to classifying the genre. As a result the HAN provides insights, from a computational perspective, into lyrical structure and language features that differentiate musical genres.