When two solid bodies are placed on the surface of a dense liquid under gravitation, they deform the liquid surface to experience a lateral capillary force between themselves that can be attractive and repulsive, depending on the wettabilities and weights of the bodies. In the present study, the lateral capillary force between two square bodies at a liquid-vapor interface has been examined using numerical simulations based on a two-dimensional two-phase lattice Boltzmann (LB) method. The particular situations were simulated, where every body was vertically constrained and had the fixed triple points at its upper or lower corners. Here, the triple point indicates the place at which vapor, liquid, and solid phases meet. The interaction force between these two bodies was calculated as a function of the separation distance, the interfacial tension, and the gravitational acceleration. The simulation results agree well with the analytical expression of the lateral capillary interaction, indicating that our LB method can reproduce the interaction force between two bodies of various wettabilities at a liquid-vapor interface in mechanical equilibrium.