I don't think it necessarily follows at all that the lieutenant of Barad-dur (as fortress/palace) was the second in command for Mordor the state (he is nowhere called the lieutenant of Mordor, and the Witch-king is repeatedly called Sauron's most powerful servant). To be honest, I don't think there was a 'chain-of-command' in the modern sense, both because of Sauron's unique nature (with his combination of power and suspicion)or indeed also that a medievalist such as Tolkien would himself have thought to arrange his world in those terms. This would be quite unusual in a tyranny or pre-modern empire, and Sauron was the ultimate tyrant. Armies would have a sort of hierarchy, of course, but not really states, outside the ruling house. Even in Gondor, people were a bit uncertain who was in charge with Denethor dead and Faramir incapacitated: Imrahil, Gandalf or Aragorn.
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