overthewing,
LVO (Low-Vis Ops) in this case refers to airport procedures when the weather goes below a certain value in the terms of visibility and/or ceiling. The exact values are commonly slightly different from airport to airport and the exact procedures do vary as well. E.g. at my base whenever Low-Vis Ops is enforced no other aircraft may commence their approach until we have reached the ramp. This inevitably slows down operation.
ATC does not need to sort out which airplanes are suitable to try an approach. The pilots are aware of their own limitations. Likely most planes going into BCN are equipped for landing given the weather presented, but not necessarily all of them. But that's for the pilot to know, not ATC.