Fair Use is for purposes of review or scholarship. The issue of Fair Use is complex. Read more here if you want to learn more about this issue that's of great importance to writers.
When To Claim Fair Use
This is a sticky situation because a lot of writers think they can quote any material as long as they provide attribution. That's an idea that can land you in the kind of hot water that requires lawyers and deep pockets. Be very careful, and read up on the subject before you quote anything.
As much as we all love our music, it's natural that we'd want to quote it in blogs and books and such. Fair Use does not apply to song lyrics. If you quote a lyric, you must have permission.
Surprisingly, it's sometimes rather simple to gain permission to use song lyrics. Several years ago, one of my friends quoted a Bob Seger song and obtained permission for free if I remember correctly. She'd tried Seger after her first choice had named a mind-boggling fee to use one of his lyrics. Of course, now he might request a huge fee also. Things change.
No Under The Radar
There are some artists who will never agree to have their lyrics used in any way. They will also diligently pursue litigation no matter how small the fish is. Don't think you can publish "under the radar" because no one knows you. That's a myth in this age of web crawlers that can find anything with a simple Google Alert or something similar.
If you want to find out who owns the rights to lyrics, visit ASCAP, the American Society of Composers, Authors and Publishers. They are a performing rights organization which licenses and collects royalties.
Professional writers need to learn the legal issues regarding what they publish in books as well as on the Internet.