High-quality environment lighting is the foundation of creating immersive user experiences in mobile augmented reality (AR) applications. However, achieving visually coherent environment lighting estimation for Mobile AR is challenging due to several key limitations associated with AR device sensing capabilities, including limitations in device camera FoV and pixel dynamic ranges. Recent advancements in generative AI, which can generate high-quality images from different types of prompts, including texts and images, present a potential solution for high-quality lighting estimation. Still, to effectively use generative image diffusion models, we must address their key limitations of generation hallucination and slow inference process. To do so, in this work, we design and implement a generative lighting estimation system called CleAR that can produce high-quality and diverse environment maps in the format of 360$^\circ$ images. Specifically, we design a two-step generation pipeline guided by AR environment context data to ensure the results follow physical environment visual context and color appearances. To improve the estimation robustness under different lighting conditions, we design a real-time refinement component to adjust lighting estimation results on AR devices. To train and test our generative models, we curate a large-scale environment lighting estimation dataset with diverse lighting conditions. Through quantitative evaluation and user study, we show that CleAR outperforms state-of-the-art lighting estimation methods on both estimation accuracy and robustness. Moreover, CleAR supports real-time refinement of lighting estimation results, ensuring robust and timely environment lighting updates for AR applications. Our end-to-end generative estimation takes as fast as 3.2 seconds, outperforming state-of-the-art methods by 110x.