Medipix and Timepix devices, installed in the ATLAS cavern, 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 proton-proton 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 timetagging, is able to resolve the time structure of the luminosity due to the collisions of individual proton bunches when integrated over an LHC fill.