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Yes you require permission from the copyright holder of the lyrics in question to reproduce them in a book. It is not treated as referenced materials. Whether you intend to profit from the book or...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/6802 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
Yes you require permission from the copyright holder of the lyrics in question to reproduce them in a book. It is not treated as referenced materials. Whether you intend to profit from the book or wherever you intend to reproduce the lyrics is entirely irrelevant. The copyright holder holds the rights to those lyrics and he/she/they can stop you from reproducing them without his/her/their permission. If the lyrics are demonstrably in the _public domain_ you can reproduce them without permission, but not copyrighted ones.