A measurement of the top quark pair (tt¯) production cross section in proton-proton collisions at a centre-of-mass energy of 5.02 TeV is presented. The data were collected at the LHC in autumn 2017, in dedicated runs with low-energy and low-intensity conditions with respect to the default configuration, and correspond to an integrated luminosity of 302 pb−1. The measurement is performed using events with one electron or muon, and multiple jets, at least one of them being identified as originating from a b quark (b tagged). Events are classified based on the number of all reconstructed jets and of b-tagged jets. Multivariate analysis techniques are used to enhance the separation between the signal and backgrounds. The measured cross section is 62.5±1.6stat−2.5+2.6syst±1.2lumi pb. A combination with the result in the dilepton channel based on the same data set yields a value of 62.3 ± 1.5 (stat) ± 2.4 (syst) ± 1.2 (lumi) pb, to be compared with the standard model prediction of 69.5−3.7+3.5 pb at next-to-next-to-leading order in perturbative quantum chromodynamics.