Continuous ion exchange is a more sustainable alternative to current methods for removing common impurities from lithium sources. In this work, we examine ion-adsorbent interactions for Mg2+ and Ca2+ with microporous titanosilicate ETS-10, an ion exchange solid with promising performance, using experimental and computational (density functional theory, DFT) methods. Ion exchange affinity for Mg2+ and Ca2+ using the Na+-form of ETS-10 are quantified from measured equilibrium isotherms, analyzed using a modified Langmuir isotherm accounting for overall stoichiometric desorption/adsorption in the cation exchange process. The equilibrium constant for ion exchange using Na-ETS-10 is greatest for Ca and decreases in order of Mg, K, and Li, respectively. These differences in ion exchange affinity are consistent with trends in DFT-derived ion exchange energies, which account for hydration and solvation of cations using a thermochemical cycle. These equilibrium constant values and ion exchange energies suggest that exchange of Ca2+, Mg2+, and K+ using Na-ETS-10 is more favorable than that of Li+. Indeed, competitive ion exchange of equimolar aqueous mixtures of Li+ and each of K+, Mg2+, or Ca2+ demonstrate selective uptake of the non-lithium cation into the solid, thereby concentrating Li+ in the aqueous solution while removing impurity cations.