The first objective of this paper is to investigate the scaling behavior of liquid-vapor phase transition in FCC and BCC metals starting from the zero-temperature four-parameter formula for cohesive energy. The effective potentials between the atoms in the solid are determined using lattice inversion techniques as a function of scaling variables in the above formula. These potentials are split into repulsive and attractive parts as per the Weeks-Chandler-Anderson prescription, and used in the coupling-parameter expansion for solving the Ornstein-Zernike equation supplemented with an accurate closure. Thermodynamic quantities obtained via the correlation functions are used to obtain critical point parameters and liquid-vapor phase diagrams. Their dependence on the scaling variables in the cohesive energy formula are also determined. Equally important second objective of the paper is to revisit coupling parameter expansion for solving the Ornstein-Zernike equation. The Newton-Armijo non-linear solver and Krylov-space based linear solvers are employed in this regard. These methods generate a robust algorithm that can be used to span the entire fluid region, except very low temperatures. Accuracy of the method is established by comparing the phase diagrams with those obtained via computer simulation. Avoidance of the 'no-solution-region' of Ornstein-Zernike equation in coupling-parameter expansion is also discussed. Details of the method and the complete algorithm provided here would make this technique more accessible to researchers investigating thermodynamic properties of one component fluids.