The correlated production of Λ and Λ¯ baryons has been studied using 4.3 million multihadronic Z0 decays recorded with the Opal detector at Lep. Lambda pairs were investigated in the full data sample and for the first time also in 2-jet and 3-jet events selected with the k⊥ algorithm. The distributions of rapidity differences from correlated ΛΛ¯ pairs exhibit short-range, local correlations and prove to be a sensitive tool to test models, particularly for 2-jet events. The Jetset model describes the data best but some extra parameter tuning is needed to improve agreement with the experimental results in the rates and the rapidity spectra simultaneously. The recently developed modification of Jetset, the MOdified Popcorn Scenarium (Mops), and also Herwig do not give satisfactory results. This study of di-lambda production in 2- and 3-jet events supports the short-range compensation of quantum numbers.