LW versions 4.13 onwards (Beta versions) send files to the recycle bin after deletion. AFAIK these are the only versions to have ever had this feature
If you're interested, you can download the Beta (current version is 4.13.2) from the usual download page.
http://www.limewire.com/english/content/download.shtml
Or, from your personal download page if you have Pro.

You might be able to get the old LW version you're looking for here
http://oldapps.com/