We have prepared colloidal suspensions of 600 Angstrom diameter latex polyballs in a lyotropic liquid crystal. The phase diagrams of the mixtures have been determined for a few values of the surfactant to water ratio. In the nematic phase, the particles remain suspended at high temperatures but undergo a gas-liquid transition at lower temperatures. The elastic constants and rotational viscosity of the mixtures in the nematic phase have been measured using the Freedericksz transition technique. They are found to be insensitive to the presence of the particles up to a few percent in the particle concentration.