Inclusive and differential cross-sections for the production of a top-quark pair in association with a photon are measured with proton-proton collision data corresponding to an integrated luminosity of 36.1 fb −1\ncollected by the ATLAS detector at the LHC in 2015 and 2016 at a centre-of-mass energy of 13 TeV . The measurements are performed in single-lepton and dilepton final states in a fiducial volume. Events with exactly one photon, one or two leptons, a channel-dependent minimum number of jets, and at least one b-jet are selected. Neural network algorithms are used to separate the signal from the backgrounds. The fiducial cross-sections are measured to be 521±9(stat.)±41(sys.) fb and 69±3(stat.)±4(sys.) fb for the single-lepton and dilepton channels, respectively.\n