When I visit my friends near there I take I-81 south to I-66 east as far as Manassas. There are a number of roads that will take you from there to Lorton without entering Washington. The Fairfax County and Prince William Parkways are two. US15 also skirts the west side of the city, although I believe some sections are now tolled near IAD airport.
Coming down from the Northeast (Baltimore, Philadelphia, New York, etc.), you're really stuck with having to cross the Potomac on the Woodrow Wilson Bridge (I-95). You could take the Captial Beltway (I-495) the other way and cross at the Cabin John Bridge, but, frankly, I think the traffic is worse. There are no other crossings of the Potomac until the Governor Nice Bride south of La Plata, Maryland, which gets one into Virginia way south and east of Lorton, aside from the fact that US 301 is full of traffic lights and congestion.
When we went from Baltimore, we took the Baltimore-Washington Parkway past the Beltway and then DC-295 through the Anacostia neighborhood where it connects to I-295, which connects directly to the Beltway at the Wilson Bridge. On our southbound trip, at about 10-11 AM, there was some stop and go traffic on DC 295, but otherwise it was pretty clear. On the northbound trip it was clear sailing all the way home. These were both on Weekdays.
If you're coming from further west, I would think that I-81 to I66 to the Fairfax Parkway would be pretty good way to go, but it's always a good idea to check Google Maps for traffic, as I-66 can have some pretty bad traffic jams, especially in the morning going east. US 15 is OK if you're coming from Frederick or Harrisburg, but note that it is not a superhighway the entire way, and, in fact parts of it are a 2-lane road, and with lights and congestion around Leesburg. From Leesburg, you need to take the Greenway to Dulles airport, where you get on the Fairfax County Parkway. The Greenway is a toll road.