It you're logged in with your Lunarpages account name, you should be able to delete folders.  Some folders, however, get "sticky".

Never delete the folders that were there when you first ftp'd to your webspace.

If you find you can't delete a folder that a script or something made, and you know it's okay to delete it, go to your CPanel, click on File Manager, and delete it from there.  That should work.