The request body you use must contain all elements that belong to a contact, which are returned through the GET method. By using this XML, you should modify only the information you would like to update, then pass the XML in your request.
To modify the contact's subscriptions to different contact lists, you need to update contents of <ContactLists> element. You must include all of the contact lists that the contact should be on. Therefore, you should add the new list subscriptions to the existing lists in the XML returned by the GET.