Estimating scene lighting from a single image or video remains a longstanding challenge in computer vision and graphics. Learning-based approaches are constrained by the scarcity of ground-truth HDR environment maps, which are expensive to capture and limited in diversity. While recent generative models offer strong priors for image synthesis, lighting estimation remains difficult due to its reliance on indirect visual cues, the need to infer global (non-local) context, and the recovery of high-dynamic-range outputs. We propose LuxDiT, a novel data-driven approach that fine-tunes a video diffusion transformer to generate HDR environment maps conditioned on visual input. Trained on a large synthetic dataset with diverse lighting conditions, our model learns to infer illumination from indirect visual cues and generalizes effectively to real-world scenes. To improve semantic alignment between the input and the predicted environment map, we introduce a low-rank adaptation finetuning strategy using a collected dataset of HDR panoramas. Our method produces accurate lighting predictions with realistic angular high-frequency details, outperforming existing state-of-the-art techniques in both quantitative and qualitative evaluations.