An edgewise iterative scheme for high order discontinuous Galerkin method in time combined with discontinuous Galerkin methods with Lagrange multiplier in space (DG-DGLM) is developed for the large system resulting from the discretization of the nonlinear hyperbolic scalar conservation laws. Convergence analysis of the iterative scheme is given for the linear problem. Newton iteration is applied elementwise over the product elements of space and time for the nonlinear problem. Several numerical examples are presented.