Over two directions in an 11-mile stretch of Highway 160 between Las Vegas and Pahrump in Nevada, helpfully closed by the local authorities.
On its first run the Koenigsegg registered a top speed of 271.2mph, beating the Veyron even while battling an incline and oncoming winds.
Last month, Lilja set a record for the fastest 0-400kph-0, doing it in 36.44 seconds from behind the wheel of the same vehicle.
The first run resulted in a very quick top speed of 437.7km/h, which took the Agera RS 4.5km to reach.
The Hennessey Venom GT, a 1451bhp Lotus Elise-based creation by a Texas-based engineering company, reached 270.49mph on the Space Shuttle landing runway at NASA's Kennedy Space Center in 2014.
The 1000kW/1371Nm Koenigsegg still had more potential though, something Lilja seemed to know quite well, as he went back for another run.
The test was then carried out using Michelin Pilot Sport Cup 2 tyres which are the tyres the Koenigsegg is sold with and are authorised for use on the road.
The Texan firm shouldn't have much to worry about if their previous performance claims hold merit, as the Venom F5 is projected to crack 301mph (484kmh).
Koenigsegg's factory test driver Niklas Lija drove Agera RS with its 1,144bhp, 5.0-litre turbo V8 to set the new record. It's also said that the Agera RS's surge of torque did not drop off after 240 miles per hour.