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The Lambda(0)(b) -> Lambda D-+(c)s(-) K+ K- decay is observed for the first time using the data sample from proton-proton collisions recorded at a center-of-mass energy of 13 TeV with the LHCb detector, corresponding to an integrated luminosity of 6 fb-1. The ratio of branching fraction to that of Lambda(0)(b) -> Lambda D-+(c)s(-) decays is measured as 0.0141 +/- 0.0019 +/- 0.0012, where the first uncertainty is statistical and the second systematic. A search for hidden-charm pentaquarks with strangeness is performed in the Lambda D-+(c)s(-) system. No evidence is found, and upper limits on the production ratio of Pc (c) over bars(4338)(0) and Pc (c) over bars(4459)(0) pentaquarks relative to the Lambda D-+(c)s(-) final state are set at the 95% confidence level as 0.12 and 0.20, respectively.