An intramolecular distribution function for lattice chains, accounting for the long range excluded volume, has been derived employing an Ornstein-Zernike-like integral equation approach, initially investigated for off-lattice chains by Curro, Blatz, and Pings. The intramolecular distributions, obtained for 16-, 30-, and 60-mers, are compared to theoretical results for the freely jointed chain model and to Monte Carlo simulation data. The new single chain intramolecular distribution function accurately matches the Monte Carlo data whereas the ideal chain structure factor overestimates the short-range intramolecular correlations. Upon increasing density the simulated intramolecular distributions gradually evolve toward the ideal chain results although the latter are never actually reached. The intermolecular distributions for athermal and interacting 30-mers at several densities have been calculated by combining the investigated intramolecular distribution functions with the lattice-PRISM theory. Furthermore, the equation of state for athermal 20- and 30-mers and the liquid-vapor spinodal for 16-mers have been investigated. It is found that the ideal chain distribution function results in unphysical thermodynamic behavior, reflected in the equation of state as well as in the liquid-vapor spinodal. The predicted intermolecular distribution is quite reasonable, considering the simplicity of the ideal chain model. The combination lattice-PRISM/excluded volume intramolecular distribution function offers at least qualitatively correct results both for the thermodynamic properties and intermolecular correlations.