Yes, I do it. WP is good for this. It is an under-recognized ability of WP.
Song title in the Title field. For the Lyrics, put them in the Write Post body.
For fields, study the Custom Fields of WP. You can attach extra facts such as Songwriter, What Albums It Is On, What Year.
Use the plugin Custom Fields Templates to add those fields in your write post area.
Use the plugin Get Custom Field Values to display those fields in your theme's single post template single.php
Other than that, you need to think of Alphabetical techniques and plugins. It is better for lyrics, while Chronological is not so good for lyrics.
Learn to alphabatize your query before The Loop in your category templates.
Also use the plugins A-Zlist (alpha sorted by a custom field), and WP-Snap (alpha glossory by first letter). TDO Mini Forms to let users submit lyrics. WP-Print by Gamerz for printable view. TTFtitles for headlines. Kafkaesqui's almost-unknown Random Line plugin, that pulls 1 random line from 1 of your posts (songs) and puts it on the homepage (a cool trick he made for my request for my lyrics sites).
I have been meaning to write up a guide on putting Lyrics sites with WP. That is my basic outline. I have spent a couple years getting to test all these options and the above are the best.
That should do it. Good luck.