Given the hints of lepton-flavour non-universality in semi-leptonic B decays, leptoquark (LQ) models with sizeable couplings to heavy-quark flavours are enjoying a renaissance. While such models are subject to stringent constraints from low-energy experiments also bounds from non-resonant dilepton searches at the Large Hadron Collider (LHC) turn out to be phenomenologically relevant. Based on the latest LHC dilepton analyses corresponding to an integrated luminosity of around 140 fb−1 of proton-proton collisions at sqrt{s} = 13 TeV, we present improved limits on the scalar LQ couplings that involve heavy-quark flavours and light or heavy dileptons. In particular, we show that effects beyond the leading order that are related to real QCD emissions are relevant in this context, since the inclusion of additional heavy-flavoured jets notably improves the exclusion limits that derive from the high-mass dilepton tails. The impact of electroweak corrections and interference effects between signal and background is also analysed. Within the POWHEG-BOX framework we provide a dedicated Monte Carlo code that allows for an on-the-fly signal event generation including all the LQ corrections considered in this article.