If it has been less than 6 months then you can get a new installer from your download page that you got when you purchased LimeWire you can check at this link
http://sales.limewire.com/support/pro_lookup.php if it has been more than 6 months since you purchased, you can save the install to a disk (hopefully you saved the installer to you hard drive) then install it on your new computer from the disk.