This work proposes a novel design method of 2-D non-separable linear-phase paraunitary filter banks (LPPUFB). Especially the two-degree vanishing moment constraint is derived for the lattice structure. In the 2 × 2-decomposition case, the authors have already derived the constraint and designed non-separable symmetric orthonormal wavelets with vanishing moments of degree two. This work extends the discussion to more general 2m_y × 2m_x-decomposition case and yields a method to impose the condition to the lattice structure. The constraint is imposed directly on design parameters so that both of the linear-phase and paraunitary property are structurally guaranteed. Since the structure adopted in this work is based on the 2-D separable DCT, 2-D separable GenLOT, a popular lattice structure of DCT-based LPPUFB, is regarded as a special case. The main advantage of non-separable systems is the directional capability. This work allows us to obtain directional non-separable LOT with two-degree vanishing moments. Some design examples are shown to verify the significance of the proposed method.