A search for four-top-quark production is presented based on the proton-proton collision data taken at sqrt{s} = 13 TeV at the Large Hadron Collider and collected with the ATLAS detector during 2015, corresponding to an integrated luminosity of 3.2/fb. Data are analysed in the single-lepton channel, characterised by an isolated high transverse momentum electron or muon and multiple jets. No significant excess of events above the background expectation is found and an observed (expected) upper limit of 21 (16) times the four-top quark Standard Model cross-section is obtained at 95% CL. Additionally, upper bounds on four-top-quark production are set in different scenarios of physics beyond the Standard Model.