It would still apply to the U.S. government. Sumter could not be relinquished without congressional approval.
And as I pointed out to rustbucket, eminent domain is a process governments use for acquiring private property for public use. Assuming for the sake of arguement that the southern secessions were legal, Sumter would then be the property of a foreign government. Eminent domain would not apply.
Sovereignty would, Liar. However asserted.
It would still apply to the U.S. government. Sumter could not be relinquished without congressional approval.
That's an internal problem of U.S. governance, something for Lincoln to work out with the Congress. Assuming Lincoln was working on a peace policy -- in which case, it would be appropriate to include State Department and receive commissioners from the departing States. Instead, Lincoln started giving orders to the Sec'y of War and the Sec'y of the Navy.