State-of-the-art controllers for active back exosuits rely on body kinematics and state machines. These controllers do not continuously target the lumbosacral compression forces or adapt to unknown external loads. The use of additional contact or load detection could make such controllers more adaptive; however, it can be impractical for daily use. Here, we developed a novel neuro-mechanical model-based controller (NMBC) that uses a personalized electromyography (EMG)-driven musculoskeletal (MSK) model to estimate lumbosacral joint loading. NMBC provided adaptive, subject- and load-specific assistive forces proportional to estimates of the active part of biological joint moments through a soft back support exosuit. Without a priori information, the maximum assistive forces of the cable were modulated across weights. Simultaneously, we applied a non-adaptive, kinematic-dependent, trunk inclination-based controller (TIBC). Both NMBC and TIBC reduced the mean and peak biomechanical metrics, although not all reductions were significant. TIBC did not modulate assistance across weights. NMBC showed larger reductions of mean than peak values, significant reductions during the erect stance and the cumulative compressive loads by 21% over multiple cycles in a cohort of 10 participants. Overall, NMBC targeted mean lumbosacral compressive forces during lifting without a priori information of the load being carried. This may facilitate the adoption of non-hindering wearable robotics in real-life scenarios. As NMBC is informed by an EMG-driven MSK model, it is possible to tune the timing of NMBC-generated torque commands to the exosuit (delaying or anticipating commands with respect to biological torques) to target further reduction of peak or mean compressive forces and muscle fatigue.