If you are wanting your ip address for using for a direct connect with a friend, then it should be located above the direct connect search box. If it's not there, then that means you're firewalled & would have great problems using direct connect anyway. What you need to do is configure your firewall to allow LW full access; instructions:
http://www.limewire.com/english/content/firewalls.shtml
To learn about direct connect & browsing, etc. please read the 3rd post in the following link:
Bitzi Web Lookup .../Direct Connect & Magnet links
IP:
http://www.whatismyip.com/