LiDAR-based perception is critical for autonomous driving due to its robustness to poor lighting and visibility conditions. Yet, current models operate under the closed-set assumption and often fail to recognize unexpected out-of-distribution (OOD) objects in the open world. Existing OOD scoring functions exhibit limited performance because they ignore the pronounced class imbalance inherent in LiDAR OOD detection and assume a uniform class distribution. To address this limitation, we propose the Neural Distribution Prior (NDP), a framework that models the distributional structure of network predictions and adaptively reweights OOD scores based on alignment with a learned distribution prior. NDP dynamically captures the logit distribution patterns of training data and corrects class-dependent confidence bias through an attention-based module. We further introduce a Perlin noise-based OOD synthesis strategy that generates diverse auxiliary OOD samples from input scans, enabling robust OOD training without external datasets. Extensive experiments on the SemanticKITTI and STU benchmarks demonstrate that NDP substantially improves OOD detection performance, achieving a point-level AP of 61.31% on the STU test set, which is more than 10$\times$ higher than the previous best result. Our framework is compatible with various existing OOD scoring formulations, providing an effective solution for open-world LiDAR perception.