There is a KLM flight that departs roughly an hour prior most days, so around 3h prior (around 15h00 or so).

Personally I wouldn't spend much time at the aeroport. The lounge isn't very big nor does it have very good food, and is frequently crowded as it is also a Priority Pass lounge so people buy their way in. I'd leave my bags at the hôtel in the morning, take the métro to somewhere more interesting to spend the day like Reston or Tysons Corner Centre, then return with enough time to retrieve your bags from the hôtel and check-in normally at Dulles.