In the international terminal at DFW there are a set of lounges for the non US airlines that are operated by a third party. They are called The Club at DFW and are located in Terminal D between Gates D21-D22. (Take a lift to the main reception.) Opening hours: Daily, approximately 4 hours prior to departure. Note you can purchase access for $35 if you don’t have a qualifying ticket or airline status.
On approaching the main reception, you will be greeted and directed to the lounge allocated to your airline. Each lounge has a flat screen outside it displaying the airline’s name so there are easy to find. In addition, there are shower facilities available on the same level as reception. The food offering is better in Qantas than BA, and both are better than the AA lounge.