Legal Question in Entertainment Law in California

Re: Copyright Law

You could record or publish these "derivative works" of the original songs only with the consent of (and probably payment to) the original composers. Unless you copy phrases from the lyrics, however, you don't need permission of the lyricist. (Songs are typically copyrighted separately as lyrics and music, and maybe not even at the same time.)

There is nothing to stop you from registering the lyrics as poetry or written work, as long as you don't associate them with a particular piece of music. In fact, a copyright is automatic when you first create a work.