The description of the concentration kinetics in the lattice fluid model used the local equilibrium representation of the distribution function of nonequilibrium states. A set of nonlinear differential-difference equations was formulated to describe the evolution of the concentration field in the system. The calculation of the correlation functions and chemical potentials applied the quasichemical approximation for nonequilibrium states. In the linear approximation, the differential equations were derived for the density region and order parameter, where the former naturally includes the kinetic diffusion coefficient and the latter includes the time of relaxation to the equilibrium state. The initial set of nonlinear difference equations was used to study the processes with high concentration gradients. The examples of these processes include a discharge of intercalation power source and phase stratification, provided that the average density in the system corresponds to unstable state in the field of the condensed-rarefied phase transition.