CERN-LHC, ATLAS. Limits on pair production of Higgs bosons in the final state where one Higgs boson (H) decays to two photons and the other to a b-quark together with its antiparticle. The search is based on 36.1 +/- 1.2 fb^{-1} of pp collisions at sqrt{s} = 13 TeV recorded in 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. Data include at least one lepton (electron or muon), at least two central jets (no $b$-jet) and two well-identified isolated photons. The search is sensitive to both resonant and non-resonant production of Higgs boson pairs. Preselection: - Among isolated photons take the two with highest pT and require ET > 0.35 * m_gammagamma and ET > 0.25 * m_gammagamma respectively; - 105 < m_gammagamma < 160 GeV. After this preselection, further three selections are applied. - At least one lepton, pT > 10 GeV, 1.37 < |eta| < 1.52 for electrons or < |eta| < for muons; - At least two central jets, |eta| < 2.5, pT > 25 GeV; - no $b$-jet tagged by 70% b-tagging woking point.