We have carried out Monte Carlo simulations of two lattice models of enzyme-activated gelation of casein micelles in order to discover how the gelation time, t(g), depends upon the enzyme concentration, [E]. Enzymes and micelles occupy the sites of a cubic lattice with periodic boundary conditions and we define probabilities for enzymes to Split kappa-casein molecules and for micelles to irreversibly aggregate. The model allows for micelles to exhibit anisotropy in their stability against aggregation. No approximations are made in solving for quantities of interest so that any disagreement with experiments are known, a priori, to be defects of the model only. For isotropic micelles, we conclude that as [E] --> 0, t(g) is-proportional-to [E]-1 for nearly all cases studied, and that, as [E] becomes very large and the probability, per Monte Carlo step, for irreversible aggregation approaches unity, t(g) --> t(g)infinity, which is very much smaller than tg obtained for small values of [E]. These results are in agreement with experimental data. Our results show that as the micelles become very anisotropic, for fixed [E] --> 0, t(g) is-proportional-to [E]-sigma where sigma almost-equal-to 0.9. However we present an argument that this is because we have not achieved a sufficiently small value of [E] so as to observe asymptotic behavior, so that we expect sigma = 1.0 for anisotropic micelles. It is possible that the use of insufficiently small values of [E] is the reason why early measurements yield a range of sigma < 1. We discuss how the model can be modified to include changes in pH or ion concentration and other phenomena.