Is the issue here not to do with the request being for the opposite runway? If I was flying to an airport with LVPs in force and a CATII/III approach, but the RVR was for example 1500m, I can't see any reason why they can or would stop you flying to CAT I mins, and frankly aside from keeping everyone in the loop there's not really reason to tell anyone anyway.
It's obviously different though if you are asking for the opposite runway, and I imagine there are various implications. I don't know if it's reasonable that an airport/ATCU might have procedures in place to say no ad-hoc runway changes during LVPs. I could definitely see a scenario if for example if it's somewhat busy and everyone else can land with the tailwind, and you want the whole operation swapped around for your approach. Depending on procedures, infrastructure, holding points etc this may just frankly not be reasonably possible without buggering up the entire thing.