micheloni - I do not think I understand your question.
The airport will operate to 'LVP's when the weather is below certain limits. It will not 'operate' to CatII or CatIII or anything. It will have an ILS which has been 'categorised' as either CatII or CatIII depending on many things. This category will be published.
If the ILS is CatII then it is not permitted to operate to limits below those for your airline's CatII approach minima, so if the ILS is notified as CatII then you should not operate to CatIII limits, but you could possibly carry out an autoland from the CatII appproach.
If these answers do not answer your question, can you try again?