A two-dimensional (2D) lattice Boltzmann method (LBM) model was developed to simulate liquid-liquid phase separation of monotectic alloys, which is controlled by the diffusive growth, the collisions and coagulations, and the Ostwald ripening of the minority liquid droplets. The present model combines the features of the multiphase flow model proposed by Shan-Chen and the mesoscopic interparticle potentials developed by Oin. In addition, a source term is introduced in the LB evolution equations to account for the phase transformation. The proposed LBM model was applied to simulate single droplet growth, coagulation of two droplets and multi-droplet growth during the liquid-liquid phase separation process of a monotectic alloy. The simulation shows that the single droplet growth in the two-liquid phase is controlled by diffusion and that the initial nonequilibrium composition approaches to equilibrium. The coagulation velocity of two droplets is influenced by surface tension, which is in accordance with the trend of the analytical prediction. It is found that the liquid-liquid phase separation process is obviously impacted by the collisions and coagulations and the Ostwald ripening of the droplets.