An accurate mechanistic understanding of solute diffusion in partially saturated clays is critical for assessing the safety of deep geological repositories for radioactive waste. In this study, a pore-scale numerical framework is developed to simulate water and ion diffusion in partially saturated clays. First, the two-phase Shan-Chen Lattice Boltzmann method is employed to establish the liquid-gas distribution in a reconstructed three-dimensional pore geometry of a clay. An equivalent solute method is also developed and validated to improve the numerical stability of the solution at the liquid/gas interface corresponding to steep variations of the concentration and diffusion coefficient of the water tracer. By using a mobility-distance relationship from molecular simulations, Fick's law is numerically solved to simulate water diffusion in nanopores, while the coupled Poisson-Boltzmann-Nernst-Planck equations are solved to simulate ion diffusion under the influence of the electrical double layer (EDL). Our model reveals that the decrease of relative effective diffusion coefficients during the desaturation is more pronounced for ions than for water, due to the additional transport pathway of water tracers in the gas phase. The obtained effective diffusion coefficients of tritiated water and ions agree well with reported data from compacted sedimentary rocks. By comparing the local electric potential and the distribution of ion concentrations in single pores, the simulation results suggest that the EDL in unsaturated clays has a more complex influence on ion distribution than under fully water-saturated conditions. This study provides critical insights into the coupled transport processes of solutes in partially saturated clays.