The Local Importance Function Transform (LIFT) method is a sophisticated automated variance-reduction technique for Monte Carlo simulation of radiation transport problems. In previous publications, the LIFT method was tested on geometrically simple problems with a coarse representation of radiation energy dependence, and the performance of the method was found to be promising when compared to traditional weight windows–based variance-reduction techniques. In this work, the LIFT method is tested on a spatially complex benchmark test problem with a more realistic representation of energy dependence (50 energy groups) and heterogeneous materials. The performance of the method in comparison with a CADIS (Consistent Adjoint Driven Importance Sampling)–based weight windows method and an analog Monte Carlo simulation is studied. A multigroup Monte Carlo code that utilizes portions of the framework of the deterministic tool Attila has been developed such that the overhead time in implementing the variance-reduction techniques is minimal. The Monte Carlo simulations are performed on an arbitrary tetrahedral mesh created by the mesh generator in Attila. A method to transfer the deterministic solution generated on a finer mesh to a coarser mesh for implementing the hybrid simulations has been developed, and the results are quantified.