A couple of people have had this problem & solved it by reverting back to Java 5. That's not an option for you if you want to use LW 5, as it needs Java 6 to run. Maybe though, you could try an older version of Java 6.
Are you using LW 5.0 or 5.1? How long has the problem been happening? Have you been able to use older versions of LW before? Has LW 5 ever worked properly?
Try installing this version of Java (JRE 6u5):
Archive: Download Java Platform Standard Edition (Java SE) 6u5
If you're using LW 5.0, you could see whether updating to 5.1 helps.
Lime Wire » Download LimeWire
Otherwise, have a look through this thread, there might be some more suggestions to help:
http://www.gnutellaforums.com/genera...see-weird.html
If you're still stuck, could you let us know your computer specifications, including video card?