We modify the projective transformation suggested earlier.(7) Within this modified transformation, the critical point and the Zeno-line of the lattice model are moved to the critical point and Zeno-line of simple liquids. Using analytical lattice calculations and numerical simulations, we show that the lattice binodals and critical isotherms transforms with sufficient accuracy into binodals and critical isotherms of real substances such as Cs, Hg, and NH3, and other model systems with real system properties such as the van der Waals equation, Lennard-Jones systems.