Polymer-RISM theory is applied to study athermal polymeric lattice fluids. The intermolecular segmental distributions and the compressibility equation of state (EoS) have been obtained within the approach for three different intramolecular distribution functions, i.e., the random flight, the non reversal random walk, and an intramolecular distribution obtained from Monte Carlo simulations. Both the intermolecular segmental distributions and the EoS are also compared to Monte Carlo simulations. From the comparison to the simulations it is seen that the polymer-RISM theory is well able to reproduce the intermolecular segmental distributions, but it underestimates the density dependence of the EoS: the EoS is worse than the classical Huggins EoS for the same model, and only for the computer simulated intramolecular distribution we find reasonable agreement between calculated and simulated EoS. The absence of liquidlike ordering effects in a lattice fluid allow us to show to what extent the deviations are due to the incomplete incorporation of excluded volume in the intramolecular distribution functions.