Solid–liquid phase diagrams are calculated for binary mixtures of Lennard-Jones spheres using Monte Carlo simulation and the Gibbs–Duhem integration technique of Kofke. We calculate solid–liquid phase diagrams for the model Lennard-Jones mixtures: argon–methane, krypton–methane, and argon–krypton, and compare our simulation results with experimental data and with Cottin and Monson’s recent cell theory predictions. The Lennard-Jones model simulation results and the cell theory predictions show qualitative agreement with the experimental phase diagrams. One of the mixtures, argon–krypton, has a different phase diagram than its hard-sphere counterpart, suggesting that attractive interactions are an important consideration in determining solid–liquid phase behavior. We then systematically explore Lennard-Jones parameter space to investigate how solid–liquid phase diagrams change as a function of the Lennard-Jones diameter ratio, σ11/σ22, and well-depth ratio, ε11/ε22. This culminates in an estimate of the boundaries separating the regions of solid solution, azeotrope, and eutectic solid–liquid phase behavior in the space spanned by σ11/σ22 and ε11/ε22 for the case σ11/σ22<0.85.