Lower limb exoskeletons (LLEs) are wearable devices that can restore the movement autonomy of paraplegic users. LLEs can restore the users’ ability to stand upright and walk. However, most of the commercially available and clinically used LLEs rely on the user maintaining balance through the use of crutches. Recent improvements in the design and control of LLEs and other legged robots allow for autonomous balance control. In this work, we implement and evaluate a momentum-based standing balance controller in the Symbitron LLE, consisting of eight active (torque-controlled) and two passive joints. We first investigate how gain tuning of the center of mass tracking control law, part of a multi-task optimal controller, affects balancing performance. We apply pushes on different device locations while in parallel-stance, compare the response for different gains, and derive heuristic guidelines for controller tuning given the control architecture, high-level goals, and hardware limitations. Next, we show how this controller successfully prescribes joint torques to the LLE to maintain balance with a paraplegic user. The LLE can autonomously balance the user and reject mediolateral and anteroposterior pushes in the order of 60 N at hip height (and 40 N at shoulder height) while standing in parallel-stance, staggered-stance with both feet at the same height, and staggered-stance with a height difference of 0.05 m between the feet. This work presents a viable control strategy for torque-controlled light-weight under-actuated LLEs to keep the balance of paraplegic users during stance, which is a necessary starting point towards autonomous balance control during gait.