Multistrange Ca, Sn, and Pb hypernuclei with Lambda Lambda pairing interaction are investigated within the Hartree-Fock-Bogoliubov approach. The unknown Lambda Lambda pairing strength is calibrated to match with the maximal value for the prediction of the Lambda pairing gap in uniform matter for densities and iso spin asymmetries equivalent to those existing in multi-Lambda hypernuclei. In this way, we provide an upper bound for the prediction of the Lambda 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-Lambda pairing for most of hypernuclei.