<p>The local discontinuous Galerkin (LDG) method, which is equipped with generalized alternating flux, is applied to solve a singularly perturbed reaction-diffusion problem in 1D. The solution to such problems typically exhibits twin boundary layers. By utilizing generalized Gauss-Radau projections, we show that the LDG method in combination with a Shishkin mesh converges optimally in both energy and balanced norms. Here, the balanced norm refers to an appropriate norm that rescales the derivative part of the energy norm, allowing each component of the true solution to be measured with the same magnitude as the perturbation parameter approaches zero. The theoretical results not only expand upon the current energy-norm convergence associated with the LDG method when utilizing purely alternating flux but also pave the way for investigating sharp approximation for the LDG method with generalized alternating flux under balanced norms. Numerical results are provided to validate our theoretical error bounds.</p>