In copyright law there is a concept known as the Fair Use Doctrine that allows authors to use quotes or other published material as part of their narrative, but it is a very controlled and there are rules.

Can I use published song lyrics in my work?

You must get permission to use another person’s lyrics in your work. You can do this by reaching an agreement for lease of the lyrics and there will likely be a cost involved depending on a number of factors including your anticipated print run and the clout of the original songwriter.

Who would I contact to get permission to use lyrics or a song?

You must contact the copyright holder or their representative. That may be the publisher, the author or both. If the author is deceased, copyright may still be held by the writer’s estate. In the US, copyright on a work exists for 70 years after the death of the writer.