This paper presents a search for physics beyond the Standard Model targeting a heavy resonance visible in the invariant mass of the lepton–jet system. The analysis focuses on final states with a high-energy lepton and jet, and is optimised for the resonant production of leptoquarks—a novel production mode mediated by the lepton content of the proton originating from quantum fluctuations. Four distinct and orthogonal final states are considered: $e$+light jet, $\mu$+light jet, $e$+$b$-jet, and $\mu$+$b$-jet, constituting the first search at the Large Hadron Collider for resonantly produced leptoquarks with couplings to electrons and muons. Events with an additional same-flavour lepton, as expected from higher-order diagrams in the signal process, are also included in each channel. The search uses proton–proton collision data from the full Run 2, corresponding to an integrated luminosity of 140 fb$^{-1}$ at a centre-of-mass energy of $\sqrt{s} = 13$ TeV, and from a part of Run 3 (2022–2023), corresponding to 55 fb$^{-1}$ at $\sqrt{s} = 13.6$ TeV. No significant excess over Standard Model predictions is observed. The results are interpreted as exclusion limits on scalar leptoquark ($\tilde{S}_1$) production, substantially improving upon previous ATLAS constraints from leptoquark pair production for large coupling values. The excluded $\tilde{S}_1$ mass ranges depend on the coupling strength, reaching up to 3.4 TeV for quark–lepton couplings $y_{de} = 1.0$, and up to 4.3 TeV, 3.1 TeV, and 2.8 TeV for $y_{s\mu}$, $y_{be}$, and $y_{b\mu}$ couplings set to 3.5, respectively.