Geometric light detection and ranging (LiDAR)--inertial simultaneous localization and mapping (SLAM) provides efficient state estimation but lacks the continuous map representation and global refinement capabilities of neural implicit SLAM, while neural implicit methods remain computationally expensive. We propose Lightweight LiDAR--Inertial Neural SLAM (LIN-SLAM), a hybrid method that couples high-rate geometric LiDAR--inertial estimation with neural implicit tracking, continual mapping, and global refinement for accurate real-time onboard SLAM. Experiments on twelve representative sequences from three datasets spanning 32-, 64-, and 128-channel LiDAR configurations show that LIN-SLAM achieves the lowest overall mean absolute trajectory error (ATE) among the evaluated state-of-the-art geometric and neural implicit methods, while substantially reducing runtime compared with existing neural implicit SLAM methods. On a Unitree Go2 equipped with an NVIDIA Jetson Orin NX and a 16-channel LiDAR, LIN-SLAM sustains real-time localization and neural mapping over a 1.47-km indoor trajectory through challenging repetitive corridor environments, with an endpoint closure error of only 0.141~m. To the best of our knowledge, LIN-SLAM is the first LiDAR--inertial SLAM system with a neural implicit backend to achieve real-time online operation on a mobile robotic platform while maintaining state-of-the-art localization accuracy. The code will be released upon acceptance.

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