We report the four diffusion coefficients for the lysozyme-MgCl2-water ternary system at 25 C and pH 4.5. The comparison with previous results for the lysozyme-NaCl-water ternary system is used to examine the effect of salt stoichiometry on the transport properties of lysozyme-salt aqueous mixtures. We find that the two cross- diffusion coefficients are very sensitive to salt stoichiometry. One of the cross- diffusion coefficients is examined in terms of common-ion, excluded-volume, and protein-preferential hydration effects. We use the four ternary diffusion coefficients to extract chemical- potential cross- derivatives and protein-preferential interaction coefficients. These thermodynamic data characterize the protein-salt thermodynamic interactions. We demonstrate the presence of the common-ion effect (Donnan effect) by analyzing the dependence of the preferential-interaction coefficient not only with respect to salt concentration but also with respect to salt stoichiometry. We conclude that the common-ion effect and the protein-preferential hydration are both important for describing the lysozyme-MgCl2 thermodynamic interaction.