I have P4 2.4 ghz and 512 mb RAM with Limewire 4.2.6 and it runs fine. Make sure you have the latest version of the Java Virtual Machine. Go here to get the latest Java VM:
http://java.com/en/download/manual.jsp
I recommend downloading the offline installation.
Also, make sure you regularly defrag your computer and clean the registry. I don't have the URL to download good defrag programs and registry cleaners right now. But if you want it you can PM or email me.