Zipping-and-assembly mechanism (ZAM) is a new mechanism describing the kinetics of protein folding. To dissect the validity of this mechanism for various protein-like systems, a prediction test based on three-dimensional HP lattice models is carried out. It is found that only the native structures of a part of protein-like models could be predicted with a ZAM-based method. The detailed comparisons between the model proteins which are predicted or failed with the ZAM-based method suggest that the ZAM is likely to be applicable for the model proteins with the weak hydrophobicity, the low contact order for native conformations, and the large separation between the energies of native state and denatured states. These observations bring us more information about the protein-like systems for which the ZAM could be applied.