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LiDAR scene generation is increasingly important for scalable simulation and synthetic data creation, especially under diverse sensing conditions that are costly to capture at scale. Typically, diffusion-based LiDAR generators are developed under single-domain settings, requiring separate models for different datasets or sensing conditions and hindering unified, controllable synthesis under heterogeneous distribution shifts. To this end, we present OmniLiDAR, a unified text-conditioned diffusion framework that generates LiDAR scans in a shared range-image representation across eight representative domains spanning three shift types: adverse weather, sensor-configuration changes (e.g., reduced beams), and cross-platform acquisition (vehicle, drone, and quadruped). To enable training a single model over heterogeneous domains without isolating optimization by domain, we introduce a Cross-Domain Training Strategy (CDTS) that mixes domains within each mini-batch and leverages conditioning to steer generation. We further propose Cross-Domain Feature Modeling (CDFM), which captures directional dependencies along azimuth and elevation axes to reflect the anisotropic scanning structure of range images, and Domain-Adaptive Feature Scaling (DAFS) as a lightweight modulation to account for structured domain-dependent feature shifts during denoising. In the absence of a public consolidated benchmark, we construct an 8-domain dataset by combining real-world scans with physically based weather simulation and systematic beam reduction while following official splits. Extensive experiments demonstrate strong generation fidelity and consistent gains in downstream use cases, including generative data augmentation for LiDAR semantic segmentation and 3D object detection, as well as robustness evaluation under corruptions, with consistent benefits in limited-label regimes.