A lattice model for ionic surfactants with explicit counterions is proposed for which the micellization behavior can be accurately determined from grand canonical Monte Carlo simulations. The model is characterized by a few parameters that can be adjusted to represent various linear surfactants with ionic headgroups. The model parameters have a clear physical interpretation and can be obtained from experimental data unrelated to micellization, namely, geometric information and solubilities of tail segments. As a specific example, parameter values for sodium dodecyl sulfate were obtained by optimizing for the solubility of hydrocarbons in water and the structural properties of dodecane. The critical micelle concentration (cmc), average aggregation number, degree of counterion binding, and their dependence on temperature were determined from histogram reweighting grand canonical Monte Carlo simulations and were compared to experimental results. The model gives the correct trend and order of magnitude for all quantities but underpredicts the cmc and aggregation number. We suggest ways to modify the model that may improve agreement with experimental values.