In the phase diagram of the protein hen egg-white lysozyme, a region is present in which the lysozyme solution demixes and forms two liquid phases. In situ observations by optical microscopy show that the dense liquid droplets dissolve when crystals grow in this system. During this process the demixed liquid region retracts from the crystal surface. The spatial distribution of the dense phase droplets present special boundary conditions for Fick's second law for diffusion. In combination with the cylindrical symmetry provided by the kinetically roughened crystals, this system allows for a full numerical analysis. Using experimental data for setting the boundary conditions, a quasi-steady-state solution for the time-dependent concentration profile was shown to be valid. Comparison of kinetically rough growth in a phase separated system and in a nonseparated system shows that the growth kinetics for a three-phase system differs from a two-phase system, in that crystals grow more slowly but the duration of growth is prolonged.