Differential and double-differential distributions of kinematic variables of leptons from decays of top-quark pairs (tt ̄) are measured using the full LHC Run 2 data sample collected with the ATLAS detector. The data were collected at a pp collision energy of s = 13 TeV and correspond to an integrated luminosity of 140 fb −1. The measurements use events containing an oppositely charged eμ pair and b-tagged jets. The results are compared with predictions from several Monte Carlo generators. While no prediction is found to be consistent with all distributions, a better agreement with measurements of the lepton p T distributions is obtained by reweighting the tt ̄ sample so as to reproduce the top-quark p T distribution from an NNLO calculation. The inclusive top-quark pair production cross-section is measured as well, both in a fiducial region and in the full phase-space. The total inclusive cross-section is found to be σtt ̄=829±1(stat)±13(syst)±8(lumi)±2(beam)pb, where the uncertainties are due to statistics, systematic effects, the integrated luminosity and the beam energy. This is in excellent agreement with the theoretical expectation.