Diffusion of a solute can be induced by the concentration gradient of another solute in solution. This transport mechanism is known as cross-diffusion. We have investigated cross-diffusion in a ternary protein salt water system. Specifically, we measured the two cross-diffusion coefficients for the lysozyme-NaCl-water system at 25 degrees C and pH 4.5 as a function of protein and salt concentrations by Rayleigh interferometry. One cross-diffusion coefficient characterizes salt osmotic diffusion induced by a protein concentration gradient, and is related to protein salt thermodynamic interactions as described by the theories of Donnan membrane equilibrium and protein preferential hydration. The other cross-diffusion coefficient characterizes protein diffusiophoresis induced by a salt concentration gradient, and is described as the difference between a preferential-interaction coefficient and a transport parameter. We first relate our experimental results to the protein net charge and the thermodynamic excess of water near the protein surface. We then extract the Stefan-Maxwell diffusion coefficient describing protein salt interactions in water. We find that the value of this coefficient is negative, contrary to the friction interpretation of Stefan-Maxwell equations. This result is explained by considering protein hydration. Finally, protein diffusiophoresis is quantitatively examined by considering electrophoretic and hydration effects on protein migration and utilized to accurately estimate lysozyme electrophoretic mobility. To our knowledge, this is the first time that protein diffusiophoresis has been experimentally characterized and a protein salt Stefan-Maxwell diffusion coefficient reported. This work represents a significant contribution for understanding and modeling the effect of concentration gradients in protein salt aqueous systems relevant to diffusion-based mass-transfer technologies and transport in living systems.