In this paper we study the asymptotic synchronization in coupled system of three-dimension nonlinear chaotic equations with various boundary conditions. We couple the nearest neighbors of each variable of equations in a squared n×n lattice. A general mathematical framework for analyzing asymptotic synchronization is given. We prove that the asymptotic synchronization occurs provided that the coupled system is pointwise dissipativeness and the coupling coefficients are sufficiently large. As an illustration of the application, particular attention is paid to the asymptotic synchronization of coupled Lorenz equations with Dirichlet, Neumann, and periodic boundary conditions, respectively. The relationship between dynamics and boundary conditions is discussed. A specific Lyapunov function is constructed to establish the pointwise dissipativeness of coupled Lorenz equations.