The Gibbs ensemble algorithm is implemented to determine the vapour-liquid and liquid-liquid phase coexistence of dilute ternary fluid mixtures interacting via a Lennard-Jones potential. Calculations are reported for mixtures with a third component characterised by different intermolecular potential energy parameters. Comparison with binary mixture data indicates that the choice of energy parameter for the third component affects the composition range of vapour-liquid substantially. The addition of a third component lowers the energy of liquid phase while slightly increasing the energy of the vapour phase.