I think the US Supreme Court will find that the gun ban in DC will stand if they look at the Washington DC proper because Washington DC is not a state, kind of like the Vatican in Rome Italy a separate government in its self with its own system if I am not mistaken.
Washington, D.C. is the capital of the United States. It is situated within and coterminous with the District of Columbia (abbreviated as "D.C."). The city and the district are located on the banks of the Potomac River and bordered by the states of Virginia (to the west) and Maryland (to the north, east and south). The city was planned and developed in the late 18th century to serve as the permanent national capital; the federal district was formed to keep the national capital distinct from the states.