LiDAR-camera extrinsic calibration (LCEC) is crucial for multi-modal data fusion in autonomous robotic systems. Existing methods, whether target-based or target-free, typically rely on customized calibration targets or fixed scene types, which limit their applicability in real-world scenarios. To address these challenges, we present EdO-LCEC, the first environment-driven online calibration approach. Unlike traditional target-free methods, EdO-LCEC employs a generalizable scene discriminator to estimate the feature density of the application environment. Guided by this feature density, EdO-LCEC extracts LiDAR intensity and depth features from varying perspectives to achieve higher calibration accuracy. To overcome the challenges of cross-modal feature matching between LiDAR and camera, we introduce dual-path correspondence matching (DPCM), which leverages both structural and textural consistency for reliable 3D-2D correspondences. Furthermore, we formulate the calibration process as a joint optimization problem that integrates global constraints across multiple views and scenes, thereby enhancing overall accuracy. Extensive experiments on real-world datasets demonstrate that EdO-LCEC outperforms state-of-the-art methods, particularly in scenarios involving sparse point clouds or partially overlapping sensor views.