Who is Sauron's second-in-command?

Question

Is the Witch king of Angmar or the Mouth of Sauron the chief lieutenant of Mordor? (similar to Darth Sidious and Darth Vader) During the War of the Ring, the Witch King leads Sauron's army in the attack to Minas Tirith. But does that mean that he is the second in command of Sauron or the chief lieutenant of Mordor? Or is it the Mouth of Sauron who is Sauron's ambassador?

Answer 1

It's not clear that Sauron has a single second-in-command. Like many medieval kings or emperors, he is used to (temporarily and conditionally) delegating power to his vassals, those who give him homage. These people may be described as his lieutenants, particularly in respect of a particular military fortification or army group of which they are holding command. They are commanding, at least in theory, in place of Sauron (they are the one "holding a place", in French lieu tenant, for him).

Thus, any important subordinate of Sauron's could be described as a lieutenant, and these could be thought of as a second-in-command in a particular place or circumstance. See Merriam-Webster's definition of lieutenant, particularly definition 1a, which in the Merriam-Webster arrangement is the oldest recorded usage.

It seems, then, that the lieutenant of the Tower of Barad-dûr is the Mouth of Sauron, and the lieutenant of Sauron's armies is the Witch-king. We see Gothmog, another of Sauron's subordinates, taking his place after his death. Gothmog, we are told, is the lieutenant of (Minas) Morgul—that is, the commander of the city:

New strength came now streaming to the field out of Osgiliath. There they had been mustered for the sack of the City and the rape of Gondor, waiting on the call of their Captain. He now was destroyed; but Gothmog the lieutenant of Morgul had flung them into the fray; Easterlings with axes, and Variags of Khand.

The Lord of the Rings, The Return of the King, Book V, Chapter 6, "The Battle of the Pelennor Fields"

There might be other lieutenants of Sauron holding other strongholds, or commanding other armies. It's not necessarily the case that any one of them is the second-in-command of Sauron.

Answer 2

Under the assumption of an organization as Matt Gutting points out, I would agree with the former answer. I have no definite knowledge that Sauron acted and ruled as such, though. Even though he did have designated lieutenants (see below) he may well have had a specific second in command as well.

Your question states both "chief lieutenant of Mordor" as well as "second in command of Sauron". For the former, place-specific, title I have no answer.

Regarding a "second in command of Sauron", the Silmarillion refer to Ringwraiths as chief among the servants of Sauron.

The slaves of the Nine Rings of Men and chief servants of Sauron

Silmarillion, Index of names.

Of these, the Witch-king of Angmar several places is referred to as the leader of the nine

"He was still in command, wielding great powers. King, Ringwraith, Lord of the Nazgûl, he had many weapons. He left the Gate and vanished."

The Lord of the Rings, The Return of the King, Book V, Chapter 6, "The Battle of the Pelennor Fields"

The Witch-king being the lord among chiefs, he would be Second-in-command of Lord Sauron.

As for the Mouth of Sauron, we have that he was 'only' the lieutenant of the Tower of Barad-dûr.

The Lieutenant of the Tower of Barad-dûr he was, and his name is remembered in no tale; for he himself had forgotten it, and he said: 'I am the Mouth of Sauron.'

The Lord of the Rings, The Return of the King, Book V, Chapter 10, "The Black Gate Opens"

If another contender to the place of second-in-command was present, I believe we would had heard of him (my assumption of course).