Differential and double-differential distributions of kinematic variables of leptons from decays of top-quark pairs ($ t\overline{t} $) 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 $ \sqrt{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 $ t\overline{t} $ 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$ {\sigma}_{t\overline{t}}=829\pm 1\ \left(\textrm{stat}\right)\pm 13\ \left(\textrm{syst}\right)\pm 8\ \left(\textrm{lumi}\right)\pm 2\ \left(\textrm{beam}\right)\ \textrm{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.