An understanding of the equilibrium critical phenomena of fluid mixtures is necessary for modeling the flow of multiphase materials. This understanding is not only required for estimating phase stability and the type of phase separation process (droplet growth or bicontinuous fluid pattern formation [12,13,14,15,16]), but also for transport properties (collective diffusion, self-diffusion, viscosity) that depend sensitively on the nature of the critical phenomena occurring in the liquid. This is natural given the existence of order-parameter (fluid composition) fluctuations that cause a mode-coupling between momentum and mass transport processes [26,27,28,29,30,31,32]. Our first task in developing the LB model for these many practical applications (involving phase separating fluid mixtures under flow conditions) is to establish the type of equilibrium critical phenomena exhibited by this model fluid mixture. While the LB models do have hydrodynamic interactions, they do not treat hydrodynamic couplings associated with non-mean field contributions to the mode-coupling between compositional and velocity fluctuations [26,27,28,29]. The theory is thus a mean-field theory also in the sense of fluid dynamics and the implications of this constraint requires further investigation.