OP - When you offload at IAD, you will be directed to midfield CBP if a connecting passenger and to the main CBP at international arrivals if not connecting. After processing (CBP and security checkpoint), you will emerge on the C concourse and walk to your new UA gate. If indeed your departure gate is D10 (highly unlikely to be certain until 2-3 hours prior to departure), it will be a hike, but easy to find. The C & D concourses are the same long concourse, with one end labeled C and the other D.

The standby on UA is a potential glitch here. Make 100% certain at check-in that your bag is tagged to its final UA destination. Even though you must cart it through CBP in all instances, if it is tagged as a connecting bag, you will go to CBP midfield for processing. If your bag is only tagged to IAD, it will be directed to international arrivals and you will reclaim it there.

Depending on the day of the week, time of day, your citizenship and whether you have Global Entry, I see a 90-minute connection as tough. A lot depends on the consequences of a misconnect. When is the next flight and is there availability if you misconnect? You will, of course, be rebooked, but LH cannot manufacture space for you.