Dynamic and thermodynamic behaviors of associating fluids play a crucial role in various science and engineering disciplines. Cubic plus association equation of state (CPA EOS) is implemented in a central-moments-based lattice Boltzmann method (LBM) in order to mimic the thermodynamic behavior of associating fluids. The pseudopotential approach is selected to model the multiphase thermodynamic characteristics such as reduced density of associating fluids. The priority of central-moments-based approach over multiple-relaxation-time collision operator is highlighted by performing double shear layers. The integration of central-moments-based LBM and CPA EOS is useful to simulate the dynamic and thermodynamic characteristics of associating fluids at high flow rate conditions, which is extended to high-density ratio scenarios by increasing the anisotropy order of gradient operator. In order to increase the stability of the model, a higher anisotropy order of the gradient operator is implemented; about 34 present reduction in spurious velocities is noticed in some cases. The type of gradient operator considerably affects the model thermodynamic consistency. Finally, the model is validated by observing a straight line in the Laplace law test. Prediction of thermodynamic behaviors of associating fluids is of significance in various applications including biological processes as well as fluid flow in porous media.