The operating carrier (United) is the relevant airline here, as opposed to the marketing carrier (Lufthansa). For checking on status, it may be helpful to note that your MUC-IAD flight is United 107, and your IAD-PHX flight is United 1947.
While Dulles is not a great gateway, you are in relative luck insofar as United has its own international arrivals facility. It may be labeled on terminal maps as FIS (Federal Inspection Service), and is found below the C Concourse at the outer midfield terminal.
United's transatlantic arrivals usually arrive at Concourse C. After you disembark the plane, follow the signs for connecting/transferring passengers. You will be processed through U.S. immigration, then collect your checked bags if any, then be processed through U.S. customs. After you go through customs, there should be a counter where you can re-check bags for your onward flight to Phoenix. You will go through a TSA check, and then exit to Concourse C.
You can check United's Flight Status website or the app to see where UA1947 has been departing from in recent days; additional historical information is also found on third parties like FlightAware and Flightstats. The great majority of United long-haul flights depart from Concourse C or Concourse D, so you probably will not need to change terminals, although it can be a long walk to the far end of D.
There is a possibility that instead of the midfield facility, you will be sent to the main International Arrivals Building (which may be labeled IAB on terminal maps). This is where passengers whose final destination is Washington go, as well as international arrivals from all other airlines. The procedure is largely the same, except that after disembarking the plane, you will ride in a "mobile lounge", and you will exit into the Main Terminal.
If this happens, you will need to go through TSA screening again at the main checkpoint, then proceed back out to the midfield terminal for your connecting flight. If it departs from the C gates, take the AeroTrain from the main terminal station. If it departs from D gates, take the mobile lounge for Concourse D. While the C and D gates are in the same building, it is a long walk from one end to the other, and you should also note that the AeroTrain station at C is irritatingly far from the gates.
This will make it much more difficult to make a two-hour connection. If you miss your flight, however, you can go to United's customer service desk, and they should be able to rebook you at no charge on the next available flight to Phoenix.