You are right. I played around with this some more after I posted my plea for help and finally got it to work. If anyone else as this problem, here's what you do:

1. Highlight the LimeWire folder and "Get Info" (File: Get Info or Flower Symbol + I)
2. Click on "Ownership & Permissions" and expand
3. Grant "Read & Write" Access to all fields (Owner, Group and Others...I'm not sure which one fixed the problem so I recommending granting full access to all 3)
4. Click "Apply to enclosed items" so you can delete all the contents of the folder
5. Now you should be able to drag & drop into the Trash