Robust depth completion is fundamental to real-world 3D scene understanding, yet existing RGB--LiDAR fusion methods degrade significantly under adverse weather, where both camera images and LiDAR measurements suffer from weather-induced corruption. In this paper, we introduce AURORA-KITTI, the first large-scale, physics-consistent synthetic RGB-LiDAR benchmark for any-weather depth completion and denoising. We further formulate Depth Completion and Denoising~(DCD) as a unified task that reconstructs clean dense metric depth from weather-corrupted RGB images and sparse LiDAR inputs while suppressing weather-induced noise. AURORA-KITTI contains over 82K weather-consistent RGB--LiDAR pairs with metric depth supervision, spanning diverse weather types, three severity levels, day/night scenes, paired clean references, lens occlusion conditions, and textual descriptions.Moreover, we provide DDCD as a strong and efficient distillation-based reference baseline. DDCD is trained on AURORA-KITTI using a frozen teacher applied to paired clean RGB images only during training; at inference, it uses weather-corrupted RGB and sparse LiDAR. Experiments on AURORA-KITTI and the real-world DENSE benchmark show that existing depth completion and foundation depth models remain vulnerable under severe weather, while DDCD improves over weather-aware retraining. Controlled experiments further show that physics-consistent adverse-weather data is the dominant driver of robustness, with clean-prior distillation providing complementary gains. Comparisons with off-the-shelf zero-shot methods use different training protocols; same-data retraining and component ablations separately quantify the contributions of weather-aware data and DDCD. Github: https://github.com/Warwick-Jocelyn/AURORA-KITTI.

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