Make sure LimeWire is not running. Open a simple text editor, such as Notepad (windows). In the open dialog, browse your hard drive for the limewire installation folder. Typically, yours will look like

C:\Program Files\LimeWire 1.6d

In this folder, look for a limewire.props file. Open it. Scroll down until you find the entry:

SHOW_TRAY_DIALOG=false

Change this to:

SHOW_TRAY_DIALOG=true

Save the document and close Notepad. Launch LimeWire and enjoy your system tray! :-)