It seems common enough for people to post lyrics on these things, usually, I would guess, because that particular song moves them or has some special meaning to them at the time. For example, this, from the song Innuendo by Queen:
You can be anything you want to be Just turn yourself into anything you think that you could ever be Be free with your tempo, be free be free Surrender your ego - be free, be free to yourself
Which incidentally is not exactly what I thought they were (change 'tempo' to temple and 'ego' to evil) before looking them up, but near enough as no matter. This song has in the past been my very favourite and still means a great deal to me, much like another song from which I recently posted lyrics. Someone else reading those may have no reaction at all, though. They may not even have heard of the song. It is even possible, I suppose, that they may have different tastes to me and actually dislike those songs, but let's not be crazy.
I do think a large part of the power of music comes from its performance, so quoting from a song will have much less of its full impact than a story or poem which can be presented in its entirety. To take an extreme example, how am I to quote from the Hungarian Dance playing now to convey to the reader the feeling of sheer vitality it carries? Unless your name is Vetinari a sequence of notes written down is not going to be as good as an actual performance.
This is my way of laying groundwork for saying that quoting lyrics is going to be more effective for an audience that already knows and has similar feelings about the song and less effective for an audience with no connection to it. That is also true for anything else, such as the already mentioned story or poem, but to a lesser extent if the whole things is presented (and if it is short enough for people not to grow bored reading). Any quoted fragments are in the same lottery as quoted lyrics though.
Have I covered everything? Yes? No? Too tired to know, so post this now and fix/add anything necessary when (if) it is identified.