Can you quote song lyrics in your book? Sure, if you're willing to pay.
Author Blake Morrison knows this to his cost. In his novel, "South of the River," he had a party at which the hosts played a number of songs and he felt it was important to cite some of the lyrics. He thought since he was using only a line or two from a handful of songs, he didn't need to bother getting permission (or paying for it).
At the last minute, his publishing house realized the permissions had not been secured and got them. Here's his account of the bill (for US readers, £1 = approx. $1.50), as relayed in an article in the Guardian:
"For one line of "Jumpin' Jack Flash": £500. For one line of Oasis's "Wonderwall": £535. For one line of "When I'm Sixty-four": £735. For two lines of "I Shot the Sheriff" (words and music by Bob Marley, though in my head it was the Eric Clapton version): £1,000. Plus several more, of which only George Michael's "Fastlove" came in under £200. Plus VAT. Total cost: £4,401.75. A typical advance for a literary novel by a first-time author would barely meet the cost."
Doesn't seem fair, does it? As Morrison points out, it's free advertising for the song and it's not like you're pirating an actual recording. But the record companies have lots of lawyers, so in this case it's better to be safe then sorry.
Morrison's solution: "[the] next time I need songs I'll make them up myself."
(For information about protecting your literary material, go to my timetowrite.com site where you'll find a helpful report on this topic.)