Large-scale dynamic Monte Carlo simulations of a lattice gas on a 2000x2000 square lattice with a Glauber-type spin flip dynamics were performed. The results are discussed in the light of classical nucleation theory (CNT) which can be fully specified for the problem due to the availability of exact values for the interfacial energy of a large nucleus, known from the Onsager solution. Several alternative (field-theoretic or nonclassical) descriptions were also considered. Special attention was paid to the pre-exponential in the cluster distribution function and to the finite-size corrections to the interfacial energies which are required in order to comply with observations. If taken literally, the CNT produces large errors when predicting either the cluster distribution function or the nucleation rate. However, at intermediate temperatures (up to 0.7 T-c) the correspondence can be substantially improved by considering the low-temperature properties of small clusters and adjusting the pre-exponential. At higher temperatures the CNT is in qualitative disagreement with the simulations. Several explanations for this, including coagulation between clusters, are proposed.