2nd in command to sauron

[Legolas]

I disagree. Khamul resided in Dol Guldur yes, but he did not lead it's armies or do anything of a commanding nature. [...]
Once that battle was over, at the parley it is stated that the Mouth of Sauron is now Sauron's lieutenant. I see no reason to doubt that. The remaining Nazgul do not have enough initiative to be able to command themselves.

The Mouth of Sauron was the Lt. of Barad-dur whether the Witch-King was live or not because the Witch-King did not reside at Barad-dur. Khamul *was* the highest power at Dol Guldur - see Gwaihir's quote above.