<p>We use magnetization measurements under pressure along with ab initio and cluster many-body calculations to investigate magnetism of the Kitaev candidate Li₂RhO₃. Hydrostatic compression leads to a decrease in the magnitude of the nearest-neighbor ferromagnetic Kitaev coupling <i>K</i>₁ and the corresponding increase in the off-diagonal anisotropy Γ₁, whereas the experimental Curie-Weiss temperature changes from negative to positive with the slope of +40 K/GPa. On the other hand, spin freezing persists up to at least 3.46 GPa with the almost constant freezing temperature of 5 K that does not follow the large changes in the exchange couplings and indicates the likely extrinsic origin of spin freezing. Magnetic frustration in Li₂RhO₃ is mainly related to the interplay between ferromagnetic <i>K</i>₁ and antiferromagnetic Γ₁, along with the weakness of the third-neighbor coupling <i>J</i>₃ that would otherwise stabilize zigzag order. The small <i>J</i>₃ distinguishes Li₂RhO₃ from other Kitaev candidates.</p>