The spin-orbit splittings A(SO)(R) of the A(2)Pi state of LiRg (Rg = Ar, Kr and Xe) complexes have been obtained from the configuration interaction calculations using relativistic effective core potentials and two-component spinors. The results confirm that the mixing between the p orbitals of the lithium atom and the valence np orbitals (and not the Rydberg orbitals) of the rare gas (Rg) atom produces a large A(SO)(R) for the A(2)Pi states at short internuclear distances. The spectroscopic constants for the ground and A states of LiRg complexes are also reported.