Discrete modeling is a concept to establish thermodynamics on Shannon entropy expressed by variables that characterize discrete states of individual molecules in terms of their interacting neighbors in a mixture. To apply this method to condensed-phase lattice fluids, this paper further develops an approach proposed by Vinograd which features discrete Markov-chains for the sequential lattice construction and rigorous use of Shannon information as thermodynamic entropy, providing an in-depth discussion of the modeling concept evolved. The development comprises (1) improved accuracy compared to Monte Carlo data and (2) an extension from a two-dimensional to a three-dimensional simple lattice. The resulting model outperforms the quasi-chemical approximation proposed by Guggenheim, a frequently used reference model for the simple case of spherical molecules with uniform energetic surface properties. To illustrate its potential as a starting point for developing g(E)-models in chemical engineering applications, the proposed modeling methodology is extended, using the example of a simple approach for dicelike lattice molecules with multiple interaction sites on their surfaces, to address more realistic substances. A comparison with Monte Carlo simulations shows the model's capability to distinguish between isomeric configurations, which is a promising basis for future g(E)-model development in view of activity coefficients for liquid mixtures.