A high coordination lattice model was recently introduced for simulating coarse-grained rotational isomeric state (RIS) chains in which the bonds have symmetric torsional potential energy functions, E(phi) = E(-phi). This symmetry was exploited in the coarse-graining and mapping onto the high coordination lattice, thereby making the procedure unsuitable (without modification) for application to chains where one or more bonds has an asymmetric torsion potential energy function, E(phi) not equal E(-phi). The necessary modification is described here, and then documented by mapping previously described RIS models for isotactic and syndiotactic polypropylene onto the high coordination lattice. Each bead on the high coordination lattice represents a monomer unit, C3H6, of polypropylene. The conditional probabilities derived from the RIS model form the basis for the acceptance of the single bead moves used in the Monte Carlo simulations on the 2nnd lattice. The simulated chains have reasonable mean-square end-to-end distances and mean-square radii of gyration. The relaxation of the end-to-end vector follows the stretched exponential behavior, exp[-(t/tau)beta], where beta=0.5 and tau is the correlation time. The elaboration retains the ability to correctly treat chains in which the bonds have symmetric torsional potential energy functions, as shown by application to polyethylene, where each bead on the high coordination lattice represents C2H4.