Medipix and Timepix devices, installed in the ATLAS cavern at the LHC, have provided valuable complementary luminosity information. Results are presented from measurements with Timepix3 (TPX3) detectors. In contrast with previously employed frame-based data acquisition, the TPX3 detector remains active continuously, sending information on pixel hits as they occur. Hit- and cluster-counting methods were used for the luminosity determination of the LHC protonproton collisions. The LHC luminosity versus time is determined using these two methods and fitted to a simple model, which incorporates luminosity reduction from single bunch and beam-beam interactions. The precision of the luminosity determination could be improved by counting the number of clusters, instead of just pixel hits. The internal precision and long-term stability of the TPX3 luminosity measurement are below 0.5%. TPX3, owing to its 1.56 ns time-tagging, is able to resolve the time structure of
the luminosity due to the collisions of individual proton bunches when integrated over an LHC fill.