The aims of this thesis project have been to determine the feasibility of hyperon reconstruction utilizing a newly developed and implemented vertex fitter based on the Lagrange multiplier method. This was achieved through simulation and subsequent analysis of the reaction specified below, detailing the production of Λ-hyperon and K+ -meson pairs from proton-proton collisions. 𝑝(4.5𝐺𝑒𝑉)𝑝 → ΛΛ𝐾+𝐾+ This reaction channel provides a more complicated topology than previous benchmark studies of the fitter performance and is of interest as it enables studies of the strong ΛΛ interaction via the femtoscopy method. For this reason, measurements of this reaction channel were among the physics goals of the HADES beam time taking place in February 2022. As such, this study has provided insight into the feasibility of performing a femtoscopy analysis on this data by reconstructing the Λ-pair using the fitter. The obtained results provide the Λ-pair reconstruction efficiency and purities based on the lower limit of expected events collected during this beamtime. As for the fitter performance, it was found from the reconstructed kinematics of the Λ-pair that the fitter can effectively remove background over most of the kinematic region. However, for low relative momentum, combinatorial background becomes especially prominent. As this region is of interest in a femtoscopy study, it has been identified as especially challenging for the developed analysis procedure.