Gait synchronization has attracted significant attention in research on assistive lower-limb exoskeletons because it can circumvent conflicting movements and improve the assistance performance. This study proposes an adaptive modular neural control (AMNC) for online gait synchronization and the adaptation of a lower-limb exoskeleton. The AMNC comprises several distributed and interpretable neural modules that interact with each other to effectively exploit neural dynamics and adopt feedback signals to quickly reduce the tracking error, thereby smoothly synchronizing the exoskeleton movement with the user's movement on the fly. Taking state-of-the-art control as the benchmark, the proposed AMNC provides further improvements in the locomotion phase, frequency, and shape adaptation. Accordingly, under the physical interaction between the user and the exoskeleton, the control can reduce the optimized tracking error and unseen interaction torque by up to 80% and 30%, respectively. Accordingly, this study contributes to the advancement of exoskeleton and wearable robotics research in gait assistance for the next generation of personalized healthcare.