This paper presents a novel, data-driven language model that produces entire lyrics for a given input melody. Previously proposed models for lyrics generation suffer from the inability of capturing the relationship between lyrics and melody partly due to the unavailability of lyrics-melody aligned data. In this study, we first propose a new practical method for creating a large collection of lyrics-melody aligned data and then create a collection of 1,000 lyrics-melody pairs augmented with precise syllable-note alignments and word/sentence/paragraph boundaries. We then provide a quantitative analysis of the correlation between word/sentence/paragraph boundaries in lyrics and melodies. We then propose an RNN-based lyrics language model conditioned on a featurized melody. Experimental results show that the proposed model generates fluent lyrics while maintaining the compatibility between boundaries of lyrics and melody structures.