Light field images capture multi-view scene information and play a crucial role in 3D scene reconstruction. However, their high-dimensional nature results in enormous data volumes, posing a significant challenge for efficient compression in practical storage and transmission scenarios. Although neural representation-based methods have shown promise in light field image compression, most approaches rely on direct coordinate-to-pixel mapping through implicit neural representation (INR), often neglecting the explicit modeling of scene structure. Moreover, they typically lack end-to-end rate-distortion optimization, limiting their compression efficiency. To address these limitations, we propose SANR, a Scene-Aware Neural Representation framework for light field image compression with end-to-end rate-distortion optimization. For scene awareness, SANR introduces a hierarchical scene modeling block that leverages multi-scale latent codes to capture intrinsic scene structures, thereby reducing the information gap between INR input coordinates and the target light field image. From a compression perspective, SANR is the first to incorporate entropy-constrained quantization-aware training (QAT) into neural representation-based light field image compression, enabling end-to-end rate-distortion optimization. Extensive experiment results demonstrate that SANR significantly outperforms state-of-the-art techniques regarding rate-distortion performance with a 65.62\% BD-rate saving against HEVC.