We evaluated the spin-exchange interactions of Li(3)RuO(4) by performing energy-mapping analysis based on density functional calculations and examined the nature of its magnetic transition at T(1) = 66 K and the divergence of the field-cooled and zero-field-cooled susceptibilities below T(2) = 32 K. Our study shows that T(1) is associated with a three-dimensional antiferromagnetic ordering, in which the two-dimensional antiferromagnetic lattices parallel to the ab plane are antiferromagnetically coupled along the c direction. We examined how the substitutional defects, Ru atoms residing in the Li sites, affect the antiferromagnetic coupling along the c direction to explain why the expected c-axis doubling is not detected from powder neutron diffraction measurements. The susceptibility divergence below T(2) is attributed to a slight spin canting out of the ab plane.