Gibbs ensemble Monte Carlo simulations are used to test the ability of the van der Waals one-fluid theory to predict phase equilibria for ternary systems of particles interacting with Lennard-Jones potentials. Simulation results for asymmetric systems are compared to theoretical results for mixtures that obey the Lorentz-Berthelot combining rules. Good agreement is found between theory and simulation far form the plait point. The theory is found to overestimate the plait point, as expected from previous studies of binary systems. Liquid-liquid equilibria in a symmetric ternary system with energy parameters deviating from the geometric mean (Berthelot) rule are also investigated at three different pressures. A three-phase region is found at high pressures. The agreement between theory and simulation is excellent for the symmetric systems studied here.