Results of computational investigations of the structural and electronic properties of the ground states of binary compounds LiBx with 0.67 ≤ x ≤ 1.00 under pressure are reported. Structure predictions based on evolutionary algorithms and particle swarm optimization reveal that with increasing pressure, stoichiometric 1:1-LiB undergoes a variety of phase transitions, is significantly stabilized with respect to the elements and takes up a diamondoid boron network at high pressures. The Zintl picture is very useful in understanding the evolution of structures with pressure. The experimentally seen finite range of stability for LiBx phases with 0.8 ≤ x ≤ 1.00 is modeled both by boron-deficient variants of the 1:1-LiB structure and lithium-enriched intercalation structures. We find that the finite stability range vanishes at pressures P ≥ 40GPa, where stoichiometric compounds then become more stable. A metal-to-insulator transition for LiB is predicted at P = 70 GPa.