In this work we study the global isomorphism between the liquid-vapor equilibrium of the hard-core attractive Yukawa fluid (HCAYF) and that of the Lattice Gas (LG) model of the Ising-like type. The applicability of the global isomorphism transformation and dependence of its parameters on the screening length of the Yukawa potential are discussed. These parameters determine both the slope of the rectilinear diameter of the liquid-vapor binodal and the Zeno-element which are the core ingredients of the fluid - lattice gas isomorphism. We compare the Zeno-element parameters with the virial Zeno-line parameters which are commonly used in the literature for the formulation of generalized law of the correspondent states. It is demonstrated that the Zeno-element parameters appear to be sensitive to the liquid state instability when the interaction potential becomes too short-ranged while the virial ones do not show any peculiarities connected with this specific of the HCAYF.

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