For "lyric sites" read "ad sites that use lyrics to attract an audience". That's where we are today.
People want lyrics. They don't want to pay for them, but they want someone to make the lyrics available for them, for free, on the Internet, forever. And they feel they are entitled to this without ads for some reason. That's where we are today.
This is broadcast publishing in a nutshell. Look at the early radio shows, they had names like "Alka-Seltzer Time," "The Fleischmann’s Yeast Hour," "The General Motors Hour" and so on. It was explicitly "we are playing music to get you to tune into our advertisement."
Free newspapers and alt-weeklies are the same. How are they supposed to function if people don't pay for them?