>> If I right click a contact list, the only option is Delete.
I think you are looking at the List in your Address Book.
You need to open your Contacts Folder from the Navigation pane.
(Typically found on the left side of the Outlook window, displaying folders like Mail, Calendar, Contacts. If you don't see it, from the main menu choose View -> Navigation Pane -> Normal).
Find the Contacts Distribution List you want in the Contacts Folder and right click on it. You should see a number of choices.
Choose Move -> Copy To Folder.
This will open the Folder Picker window. Select the Contacts folder and [OK].
You should now have two copies of the List. Double click on the new one.
This should open the List in a new window showing the contacts.
Click in the "Name" field at the top and give it a new name. Click the windows close "X".
This should popup a "save changes" window.
Click [Yes].