A recently introduced method for coarse-graining standard continuous Metropolis Monte Carlo simulations of atomic or molecular fluids onto a rigid lattice of variable scale [X. Liu, W. D. Seider, and T. Sinno, Phys. Rev. E 86, 026708 (2012)] is further analyzed and extended. The coarse-grained Metropolis Monte Carlo technique is demonstrated to be highly consistent with the underlying full-resolution problem using a series of detailed comparisons, including vapor-liquid equilibrium phase envelopes and spatial density distributions for the Lennard-Jones argon and simple point charge water models. In addition, the principal computational bottleneck associated with computing a coarse-grained interaction function for evolving particle positions on the discretized domain is addressed by the introduction of new closure approximations. In particular, it is shown that the coarse-grained potential, which is generally a function of temperature and coarse-graining level, can be computed at multiple temperatures and scales using a single set of free energy calculations. The computational performance of the method relative to standard Monte Carlo simulation is also discussed.