I-66 inside the Beltway is a nightmare, and quite odd considering that being such a major highway, it is only two lanes in each direction upon entering DC through Arlington County. I think widening it by one lane is a very smart proposal, although any more than three lanes in each direction would be devastating to the area. As of now, I-66 inside the Beltway is really aestetically pleasing, there is new signage, a sound wall which seems to blend in with the surrounding trees, and the median is well landscaped with the Metro Orange line running through the middle. Hopefully adding a third lane wouldnt cause much damage to the bordering landscaping.
A suggestion - If a third lane is added, I think it should be devoted to exiting and entering the highway only, allowing for two through lanes. The third lane could be an "exit only" lane and be consistent for the entire stretch of I-66 in Arlington County. This would allow for more space for entering vehicles to merge into the travel lanes, since currently these lanes are very short.
From what I've read, building I-66 in Arlington County in the 80s was nearly impossible and allowed only if it would be four lanes total. It seems to be a difficult and prolonged debate to widen the road, and although necessary, may not happen in the near future due to the fierce NIMBY's and Arlington's mass-transit oriented stigma - which isn't a bad thing, but very difficult to pursuade when wanting to widen an interstate.