In this letter, we propose a simplified version of lattice factorization for linear-phase perfect reconstruction filter bank (LPPRFB) derived in [1], The proposed new lattice structure spans the same class of LPPRFB as presented in [1], while substantially reducing free parameters in nonlinear optimization and saving computation cost in hardware implementation. To further address the importance of our proposed structure, we generalize our factorization to multidimensional LPPRFB (MD-LPPRFB), and show its effectiveness.