The Standard Model of particle physics provides predictions of many fundamental processes. One of them is the existence of charmless processes involving only baryons, namely charmless purely baryonic decays of baryons. Yet none of these decay modes has been experimentally observed so far. Following theoretically predicted branching fractions, the LHCb experiment is currently the only one capable of measurements concerning these rare decays. The work presented in this thesis describes the measurement techniques and the results of the study of Lambda-b baryon decays to a charmless baryonic final state using the LHCb detector involving the rare Lambda-b -> Lambda p pbar and Xib0 -> Lambda p pbar decays. The significance of existence of the Lambda-b -> Lambda p pbar signal channel is found to be 4.82 sigma, constituting the first evidence of existence of this channel. In the case of the Xib0 -> Lambda p pbar channel the found significance is 2.26 sigma, which is compatible with the non observation of this channel with the present level of statistics. Preliminary measurements of branching fraction of Lambda-b -> Lambda p pbar are reported. In addition, the production of Scintillating Fibre (SciFi) Tracker, an essential part of the upgrade of the LHCb detector, is also discussed.