The hadron particle identification provided by the RICH system in LHCb over a momentum range of 2.6-100 GeV/c has been a key element of the success of the experiment and will remain equally important for Upgrade II. With luminosities expected up to 7.5 times those expected for Upgrade I and 75 times those realised in the past, maintaining the current excellent particle identification performance demands a substantial improvement in the precision of the measurements of the space and time coordinates of the photons detected in the RICH. It will require a readout strategy with high-resolution timing information and making significant improvements in the resolution of the reconstructed Cherenkov angle.