We test the theoretical free energy surface (FES) for two-step nucleation (TSN) proposed by Iwamatsu [J. Chem. Phys. 134, 164508 (2011)] comparing predictions of theory to numerical results FES recently reported from Monte Carlo simulations TSN in a simple lattice system [James, et al., J. 150, 074501 (2019)]. No adjustable parameters are used make this comparison. That is, all evaluated direct...