The system used by most current aircraft (ILS) in foggy weather relies on there only being one aircraft flying down the approach at any one time
As far as I'm aware, the main constraint during LVPs is the requirement for the preceding lander to have vacated not just the runway, but the Localiser Sensitive Area (LSA), before landing clearance can be given to the following aircraft.
That clearly increases the approach spacing requirement, but not to the extent that only one aircraft can be on the ILS at any given time. For example on Monday morning, ATC at Heathrow were landing about 28 aircraft per hour on 09L during LVPs, which equates to just under 6nm spacing at 160kts.