This paper presents a search for exotic decays of the Higgs boson into a pair of new pseudoscalar particles, HΓ’β βaa, where one pseudoscalar decays into a b-quark pair and the other decays into a Γβ-lepton pair, in the mass range 12Γ’β°Β€maΓ’β°Β€60 GeV. The analysis uses pp collision data at s=13 TeV collected with the ATLAS detector at the LHC, corresponding to an integrated luminosity of 140 fbΓ’Λβ1. No significant excess above the Standard Model (SM) prediction is observed. Assuming the SM Higgs boson production cross section, the search sets upper limits at 95% confidence level on the branching ratio of Higgs bosons decaying into bbΓΒ―Γβ+ΓβΓ’Λβ, B(HΓ’β βaaΓ’β βbbΓΒ―Γβ+ΓβΓ’Λβ), between 2.2% and 3.9% depending on the pseudoscalar mass.