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Multi-strange Ca, Sn and Pb hypernuclei with ΛΛ pairing interaction are investigated within the Hartree-Fock-Bogoliubov approach. The unknown ΛΛ pairing strength is calibrated to match with the maximal value for the prediction of the Λ pairing gap in uniform matter for densities and isospin asymmetries equivalent to those existing in multi-Λ hypernuclei. In this way, we provide an upper bound for the prediction of the Λ pairing gap and its effects in hypernuclei. The condensation energy is predicted to be about 3 MeV as a maximum value, yielding small corrections on density distributions and shell structure. In addition, conditions on both Fermi energies and orbital angular momenta are expected to quench the nucleon-Λ pairing for most of hypernuclei.

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