The lithium-boron system has been extensively studied due to the practical importance of Li-B alloys as anode materials for the production of lithium batteries. However, many questions remained unexplained, and the phase diagram has not been determined. Some ambiguities also remained regarding the existence of a LiB3 compound and the dissolution of boron in lithium melt. To resolve these questions an approach using ab initio molecular orbital (MO) calculations on the Hartree-Fock (HF) level of theory is presented. Stability and rules of bonding for lithium-boron clusters were calculated using STO-3G, 3-21G, and 6-31G* basis sets. The calculations enabled a formulation of the rules of bonding in lithium-boron clusters which gave a suggestions to the possible mechanism of the interaction of molten lithium with crystalline boron. Experimental evidence based on chemical and X-ray diffraction analyses, supporting the results of MO calculations, is also given and a new explanation, which covers all experimental and theoretical data about the processes which occur during the heating of the lithium-boron mixture in the temperature range 300-400 degrees C is presented.