In this article, a method based on the multiphase lattice Boltzmann framework is presented which is applicable to liquid-vapor phase-change phenomena. Both liquid and vapor phases are assumed to be incompressible. For phase changes occurring at the phase interface, the divergence-free condition of the velocity field is no longer satisfied due to the gas volume generated by vaporization or fluid volume generated by condensation. Thus, we extend a previous model by a suitable equation to account for the finite divergence of the velocity field within the interface region. Furthermore, the convective Cahn-Hilliard equation is extended to take into account vaporization effects. In a first step, a D1Q3 LB model is constructed and validated against the analytical solution of a one-dimensional Stefan problem for different density ratios. Finally the model is extended to two dimensions (D2Q9) to simulate droplet evaporation. We demonstrate that the results obtained by this approach are in good agreement with theory.