Quoted

Neither SongBird or LyricFetcher is the responsible for the random lyric fetching, but lyricsplugin.com.

The solution is really simple:
get a text editor, and open:
/home/[username]/.songbird/[profiledir]/extensions/{248e3e8b-5a5c-4e7e-9bef-6720255e36e0}/chrome/content/lm_fetcher.js
at line 66 you will find something like this:

var url = "http://www.lyricsplugin.com/wmplayer03/plugin/content.php?"
+ "artist=" + returnartist
+ "&title=" + returntitle
+ "&time=" + timestamp
+ "&hash=" + id;

now at the line
+ "&time=" + timestamp change time to timestamp

[SAVE]
now open the pane.js from the same dir and do the same somewhere at line 370.
[SAVE]
[restart songbird]

Voilá!