LVP are the procedures that the airport needs to put into effect below certain predefined visibility or RVR and sometimes even a ceiling. Some airports like EHAM introduce LVP well above 400 m RVR, as the ability to guide traffic also depends on the visibility from the tower. The controllers in the tower may well be in the cloud layer even though below that layer the RVR is still well above 400m. In this case the LVTO procedure for the operator doesn’t need to be applied, as it applies only to the TO phase and the RVR or even VIS (usually VIS is used when RVR > 1500m) is well above the LVTO value. However, stopbars may well be used by controllers to guard runways and ensure adequate separation, as they are part of the airport’s LVP requirements and must be obeyed, even if the RVR/VIS is obviously way above 400m. LVP will be announced on ATIS if in force. Some RWYs may be excluded when LVP are in force, as the lack of adequate lighting for lateral guidance may preclude their use. They will simply not be available for TO or LDG, but could well be In use by a towed A/C. As these RWYs usually lack stopbars, caution must be taken.

LVTO are the approved operator’s procedures and depend on A/C type as well: enhanced vision systems can bring the allowable RVR down as they supplement the required guidance during the TO roll. Conversely, a CAT II or III approach may very well be clown, including the autoband for CAT III, by request of the crew, even in solid VMC conditions. ATC will ensure the LOC sensitive area’s to be clear of other traffic to enable a safe approach for operational reasons (e.g. A/C systems validaties or crew . No LVP will be declared in operation for the airport in this case. 550m is a minmum RVR value to start a CAT I approach. But even if the RVR value falls below 550m after passing the FAP, the crew may continue the approach to CAT I minima in the hope that the required visual references will be achieved at that point to continue (to land). LVTO has nothing to do with the type of approach that the operator may fly. It describes Take-Off procedures only. Whether approaches below 550 m may be flown, depends firstly on the A/C capability and secondly on the license endorsements and currency of the crew.

After the above has been digested, I do have a side note...
To make matters more complicated, the All Weather Operations, including LVO rules, will be changed in due time by EASA.
If interested, you may want to read through this:

https://www.easa.europa.eu/en/document-library/agency-decisions/ed-deci…

And this

https://www.easa.europa.eu/en/downloads/136718/en

Obviously I personality have no operational experience with these near-future rules. What I do understand is that the classic regulations will still apply, but capably equipped aircraft and certified and authorised pilots and operators may start using these new regulations and AMC procedures. Many airline type aircraft will not be (immediately) technically capable and will need to carry on using the legacy procedures. But the generally technically more advanced business jets could theoretically fly according to the new regulations. However, the training in simulators must be completed as one part of an extensive prior approval by the local authority to operate under the new rules. It seems very likely that training centres will be lagging far behind in providing the necessary training programmes for many months to come.
“LVO”, “CAT II” and “CAT III” as license endorsements will need to represent a totally different context or disappear altogether. No FCL details that I know of have been published so far.