This paper presents a methodology for determining the geometric center and edges of a lane using intensity scans from a downward-facing LiDAR. This method is particularly useful for creating a baseline reference path for map building or autonomous vehicle control in path-following scenarios. For this work, each laser scan is sequentially aligned to create a top-down, bird's-eye view image of the road. Using image processing techniques, including image thresholding and the Hough Transform, the lane markers are extracted. All scans are re-aligned by the painted lanes under the assumption that the painted lines are continuous and linear in lane centerline s-coordinate. The extrema (peaks and valleys) of each LiDAR intensity profile in the lateral direction are extracted using an optimal extrema filter to determine the location of the painted lane markers. The lane center is determined by averaging the post-processed and aligned left and right lane marker positions. The algorithm is experimentally validated over multiple traversals of a one-mile test track with ground truth validation using a differential GPS. Over repeated traversals, the geometric center of the lane is determined to a lateral error (1-σ) of 7 mm. The results suggest that this process could be used as a validation step for roadway design specifications, to assess lane-keeping variation errors in human- and computer-driven vehicles, to assess situation- and location-specific repeated deviations from lane center, and to even evaluate the smoothness of the lane-painting process.