A second type of literary music would be music that is about literature, rather than from it, if that makes sense to anyone. ("Paperback Writer" by the Beatles, anyone?) This would include songs that are about authors, the writing process, etc. In my experience, music of this type is using writing as a metaphor for life in general.
The final type of literary music is, in my opinion, less pervasive as well as more difficult to define. This would be music that is neither from literature nor about it, but of it. This would be music that is distinctly "literary" in its approach to story telling and rhyme schemes, that has a higher level of vocabulary, that reads like a poem when it's not put to music. Suffice it to say, it may be difficult to identify if a song fits in this category, but it isn't as hard to tell if a song doesn't belong. If a song rhymes "you," "too," "do," and "you," it probably doesn't qualify. ("It's tearin' up my heart when I'm with you, / But when we are apart, I feel it too, / And no matter what I do / I feel the pain... with or without you" is not exactly literary.)
My favorite example of this kind of music is by The Decemberists, a folk-rock band from Portland, Oregon. The songwriter for this band, Colin Meloy, was an English major, and his songs are about under-dog characters (chimney sweeps, pirates, and failed athletes) and tell a real story. Meloy employs complex rhymes and meter so the songs, even if you are just reading the lyrics, scan like poems. For example, here's one of the verses from the song "We Goth Go Down Together": "Meet me on my vast veranda / My sweet, untouched Miranda / And while the seagulls are crying / We fall but our souls are flying." If I could write music, I would want it to be like this. As it is, The Decemberists are one of my favorite bands to play on my guitar. You should listen to them if you don't already. (Here's their website: http://www.decemberists.com/index.html)