The free volume model is probably the most successful model for predicting the diffusivity of small molecules in polymers. However, the experimental procedure for parameterizing the model is not trivial and in fact extremely time consuming. In this work, we propose a much less time consuming approach for the parameterization step. In particular, we carried out isobaric-isothermal molecular dynamics simulations to generate thermodynamic data of a few selected polymer/solvent systems and used the data to parameterize the corresponding Sanchez-Lacombe equation of state (SLEOS). The characteristic parameters of the SLEOS were then used in the parameterization of the lattice free volume (LFV) model so that diffusivity of the solvents in a polymer was then determined. To illustrate the newly proposed approach, we used poly(vinyl alcohol) and water, ethanol and benzene over a concentration range of 1-20 wt% and a temperature range of 270-370 k. We found that the LFV model was much easier to be parametrized in the aforementioned approach and yielded predictions much better than that of the well-known Mackie-Meares model. We also demonstrated that the two adjustable parameters of the LFV model are related to the size of the solvent molecules and their interaction with the polymer.