Therefore, LVP's by definition, would only be required at airports with CAT II or CAT III operations, or departures below 550 RVR, right?
I don't know about the rest of the world but in Australia this is not correct. LVP are required whenever any part of the manoeuvring area cannot be visually monitored by the tower due weather. LVP are applied to ground traffic to protect aircraft movements. There may be a situation when the RWYs are in the clear but TWYs in fog. In this case vehicles are restricted with blanket clearances cancelled and works vehicles removed from the area. Aircraft under tow may require an escort from safety vehicles.