Lattice models of gapless domain walls between twisted and untwisted gauge theories of finite group G are constructed systematically. As simple examples, we numerically studied the gapless domain walls between twisted and untwisted Z_N(with N<6) gauge models in 2+1D using the state-of-art loop optimization of tensor network renormalization algorithm. We also studied the physical mechanism for these gapless domain walls and obtained quantum field theory descriptions that agree perfectly with our numerical results. By taking the advantage of the systematic classification and construction of twisted gauge models using group cohomology theory, we systematically construct general lattice models to realize gapless domain walls for arbitrary finite symmetry group G. Such constructions can be generalized into arbitrary dimensions and might provide us a systematical way to study gapless domain walls and topological quantum phase transitions.