A decorated lattice model, that consists of decorated bonds and orientational configurations of basis in the decorated cell is presented with the use of arbitrary directionality and temperature-independent interaction energies of sites to calculate the closed-loop coexistence curves of two equilibrated binary liquid phases. For mixtures containing hydrogen bonding compounds, the closed-loop diagrams obtained by the decorated lattice model are in fair agreement with experiments in the size, the shape and the flatness near the lower consolute solution temperatures, and fairly reproduced for pyridine derivatives-water mixtures. The directional interaction energies between unlike molecules, representing the strong interactions such as hydrogen bonding, are found responsible for the enhanced miscibility below the lower consolute solution temperatures. Finally, an application of the modified solution model, based on the effective interaction energies is demonstrated in the prediction of the closed-loop behaviors.