A few clarifications:
Are you flying Lufthansa into Dulles? Lufthansa arrives into the B gates.

Or, are you flying a Lufthansa codeshare operated by United, arriving at the D gates? (Which should go to the C gates)

If you are arriving on Lufthansa, and therefore clearing immigration in the main terminal, and then departing out of the A gates, you cannot take the mobile lounge to them. You can either walk or take the AeroTrain.
If you are arriving on United, you might clear immigration in the C/D terminal, and then can possibly take the mobile lounge from D to A.

This thread gets more attention and has many details: Consolidated IAD connection time/logistics-Domestic & International