IAD won't be your problem. If you're ontime, you'll have to run, but you'll be fine.

Very slim chance you will make your LHR conx. You'll need to go either through FCC (worse) or C&I and then recheckin and clear security at T2 for your LH flight to STR.

I'd advise against this. LH will probably accomodate you, but will blame UA among other things before putting you on a later flight.