Forget a class action lawsuit. It's not some court's responsibility to decide one way or another. It's already been decided by the Framers of The Constitution.
Article 1, Section 8, Clause 17 reads thus:
To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of Particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings;--
This is a wordy way of saying the federal government has no business owning or managing any property outside the ten square miles that make up Washington, D.C., and forts and ports.
KrisAnne Hall explains it a lot better than I can...