[Eurytus]

You missed the point - if the Mouth of Sauron was higher in rank than these two Nazgul, he would've been in charge of Dol Guldur or Minas Morgul instead.

I never disputed that the Witchking was ranked higher. The Lieutenant quote comes from after the Witchking's demise.
There is no indication whatsoever in the books that Dol Guldur would be a more senior post than Barad Dur.

quote:
--------------------------------------------------------------------------------
I was discussing whether he was now the lieutenant of the whole of Sauron's forces which his statement suggests he is.
--------------------------------------------------------------------------------

The Mouth had an obviously exaggerated opinion of himself.

Since he states the fact that he is to be Sauron's lieutenant to be a fact and there is NOTHING in the text to dispute this, your statement above is unfactual and therefore not really applicable.

Sauron would put his will behind them in a later attack following the Witch-King's fall.

When did this occur? The Nazgul did not command the battle of the pelenor fields after the Witchking died and it is extremely unlikely that they were commanding the battle in front of the black gate from the air. This would hardly be efficient. So which battle did they command?