From U.S. v. Class, written by Judge Thomas Griffith and joined by Judges Davis Sentelle and Sri Srinivasan:
The Supreme Court has been careful to note that “longstanding prohibitions” like “laws forbidding the carrying of firearms in sensitive places such as schools and government buildings” remain “presumptively lawful.” Heller I, 554 U.S. at 626, 627 n.26…. [T]he same security interests which permit regulation of firearms “in” government buildings permit regulation of firearms on the property surrounding those buildings as well…
First, though it is open to the public, the Maryland Avenue parking lot may be used during working hours only by Capitol employees with a permit. This makes the area a potential stalking ground for anyone wishing to attack congressional staff and disrupt the operations of Congress. The operation of the national legislature depends not only on the ability of members of Congress and their staff to conduct business inside the Capitol, but also on their ability to freely and safely travel to and from work. The same special security concerns that apply to the employees while in the Capitol apply when they walk to and from their cars on Capitol property.
Second, the lot is close to the Capitol and legislative office buildings. Class possessed a firearm less than 1,000 feet away from the entrance to the Capitol, and a block away from the Rayburn House Office Building. Although there is surely some outer bound on the distance Congress could extend the area of protection around the Capitol without raising Second Amendment concerns, Congress has not exceeded it here.
Finally, as the owner of the Maryland Avenue lot, the government—like private property owners—has the power to regulate conduct on its property. See [Adderley] v. Florida, 385
U.S. 39, 47 (1966) (observing in the free-speech context that the government, “no less than a private owner of property, has power to preserve the property under its control for the use to which it is lawfully dedicated”); cf. Bonidy v. U.S. Postal Serv., 790 F.3d 1121, 1126 (10th Cir. 2015) (observing that when the U.S. Postal Service acts “as a proprietor rather than as a sovereign, [it] has broad discretion to govern its business operations according to the rules it deems appropriate”).
Thanks to Charles Nichols for the pointer.