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Ab initio modeling of the Li-B-H system and analysis of the available experimental data on the Li_xB_1-x compound (x ≈ 0.53) have allowed us to identify a potential route for the synthesis of hydrogen-rich LiBH (5.4 wt. %) and LiBH₂ (10.2 wt. %) phases. The feasibility of their formation is based on the strength of the boron-boron bonds in the parent material Li_xB_1-x: One could expect its decomposition into lithium hydride and elemental boron upon hydrogenation to be hindered by the high kinetic barriers associated with breaking the boron chains. The proposed phases have heats of reaction of 70-90 kJ/mol H₂, higher than the desired values for hydrogen storage applications. We discuss the possibility of improving the energetics of the hydrogen (de)sorption via substitutional doping of Li_xB_1-x.