Having a quick look at Wikipedia reveals that you need a license for publishing them:
Currently, there are many websites featuring song lyrics. This offering, however, is controversial, since some sites include copyrighted lyrics offered without the holder's permission. The U.S. Music Publishers' Association (MPA), which represents sheet music companies, launched a legal campaign against such websites in December 2005, the MPA's president, Lauren Keiser, said the free lyrics web sites are "completely illegal" and wanted some website operators jailed.
So this is not a misjudgement from Apple, they even protect you in some way from being sued by a random law company (for using copyrighted material without permission).
Regarding other lyrics apps on the AppStore: I assume they have a license. At least LyricFind
does, as you could obtain a license for publishing lyrics from them.