This letter presents a framework for the target-less extrinsic calibration of stereo cameras and light detection and ranging (LiDAR) sensors with a non-overlapping field of view (FOV). In order to solve extrinsic calibration problems under such challenging configurations, the proposed solution exploits road markings as static and robust features among the various objects that are present in urban environments. First, this study utilizes road markings that are commonly captured by the two sensor modalities to select informative images for estimating the extrinsic parameters. In order to accomplish stable optimization, multiple cost functions are defined, including normalized information distance (NID), edge alignment, and plane fitting cost. Therefore, a smooth cost curve is formed for global optimization to prevent convergence to the local optimal point. We further evaluate each cost function by examining parameter sensitivity near the optimal point. Another key characteristic of extrinsic calibration, repeatability, is analyzed by conducting the proposed method multiple times with varying randomly perturbed initial points.