You will also have a claim for EUR 600 because the delay into IAD will be greater than four hours. In addition to the hotel, you may also claim reasonable meals.
I would not plan on LH reimbursing you more than a mid-range airport hotel at LHR (which you ought to document). This does not preclude you from staying downtown, but the difference between LHR-area and what you obtain will likely be out of your pocket.