Ok, I'm getting closer. Here is my code so far. It dumps a string of the Mailing Lists to the page. The values look good. Now to figure out how to correctly sort by list name and turn the XML into a list.
public ActionResult MailingLists()
{
svcMailListAdmin.PreInvoke();
svcMailListAdmin.AddParameter("AuthUserName", SM_AuthUserName);
svcMailListAdmin.AddParameter("AuthPassword", SM_AuthPassword);
svcMailListAdmin.AddParameter("DomainName", SM_DomainName);
svcMailListAdmin.Invoke("GetMailingListsByDomain");
svcMailListAdmin.PostInvoke();
var resultStr = svcMailListAdmin.ResultXML;
var types = from x in resultStr.Root.Descendants("listNames")
orderby (string) x.Attribute("string")
select x.Value;
return View((object)types.Single());
}