The Gibbs ensemble simulation technique is used to investigate the ability of van der Waals 1-fluid theory to predict phase equilibria for binary Lennard-Jones mixtures. Simulation data for highly asymmetric mixtures with size and energy parameter ratios equal to 1.00, 0.5, 0.4, 0.35 and to 0.5, 0.33, 0.25 respectively are compared to theoretical results for cases in which unlike-pair interactions follow the Lorentz-Berthelot combining rules. Additional comparisons are made for vapour-liquid and liquid-liquid equilibria of mixtures with energy parameter deviating from the geometric mean (Berthelot) rule, and for vapour-liquid and gas-gas equilibria of mixtures with size parameter deviating from the arithmetic mean (Lorentz) rule. Good agreement was found between theory and simulation when the energy parameter deviates from the Berthelot combining rule. The agreement is less satisfactory when the size parameter deviates from the Lorentz rule, especially for the case of gas-gas equilibria.