A search for a hypothetical heavy scalar particle, X, decaying into a singlet scalar particle, S, and a Standard Model Higgs boson, H, using 140 fb$^{−1}$ of proton-proton collision data at the centre-of-mass energy of 13 TeV recorded with the ATLAS detector at the LHC is presented. The explored mass range is 300 ≤ m$_{X}$ ≤ 1000 GeV and 170 ≤ m$_{S}$ ≤ 500 GeV. The signature of this search is one or two leptons (e or μ) from the decay of vector bosons originating from the S particle, S → W$^{±}$W$^{∓}$/ZZ, and two photons from the Higgs boson decay, H → γγ. No significant excess is observed above the expected Standard Model background. The observed (expected) upper limits at the 95% confidence level on the cross- section for gg → X → SH, assuming the same S → WW/ZZ branching ratios as for a SM-like heavy Higgs boson, are between 530 (800) fb and 120 (170) fb.[graphic not available: see fulltext]