We consider solving large-scale Lyapunov equations for multi-agent system. Focusing on the Kronecker product in the Lyapunov equations, we use third order tensors and its operations, which are useful to decrease memory requirements. In this paper, we propose the modified GMRES method for the Lyapunov equations which computes using third order tensor. Moreover, we display numerical examples of the proposed GMRES method and confirm convergences of that.