Limits on pair production of scalar leptoquarks, each decaying into either an electron or a muon and a top quark. The search is based on 139.0 $\pm$ 2.4 fb$^{-1}$ of pp collisions at $\sqrt{s}$ = 13 TeV recorded in 2015-2018 with the ATLAS detector at the CERN Large Hadron Collider. Data are analysed in the fully hadronic top quark final state, with a focus on the high LQ mass regime for which the top quarks tend to be boosted. The search results are interpreted to provide a limit on the leptoquark mass. Mass limits on leptoquark pair production are also set as a function of the leptoquark decay branching ratio into a charged lepton and a top quark, as opposed to a neutrino and a bottom quark. Basic event selection: - == 2 opposite-sign same-flavour leptons: pT > 100 GeV, in fiducial volume, isolated from jets - >= 2 large-radius jets - dilepton invariant mass > 120 GeV A parameterized boosted decision tree classifier is used to optimize the sensitivity to LQ signal, using event kinematics and jet substructure variables (see paper).