Platooning of connected and automated vehicles provides significant benefits in terms of energy efficiency, traffic throughput, and, most critically, safety. These safety benefits depend on string stability, which dictates how disturbances propagate along a vehicle string. Although longitudinal string stability has been extensively examined, lateral string stability, which governs the propagation of path-tracking errors that can lead to unsafe deviations from the desired path, remains underexplored. Its importance is growing as autonomous vehicles increasingly depend on onboard sensing and map-free navigation, where sensor occlusions and tight formations amplify safety risks. This paper presents a framework for lateral string stability that focuses directly on safety-critical, path-relative tracking errors and enables consistent comparison across vehicles that follow the same planned path. The key element of the framework is an arc-length (Eulerian) viewpoint, a departure from traditional analyses, that clarifies how tracking errors at a given point on the path propagate from one vehicle to the next. Building on this foundation, we propose the definition of L2 lateral string stability along with two control strategies: a feedback-feedforward strategy that relies solely on onboard sensing, and a novel learn-from-predecessor strategy that makes use of vehicle-to-vehicle communication. Both strategies are analyzed for lateral string stability with respect to two error measures: tracking error vector and lateral (cross-track) error. Our results show that onboard sensing alone cannot guarantee attenuation of path-tracking errors, imposing a fundamental safety limitation, while V2V communication enables true error attenuation. The analysis further identifies structural controller requirements, showing that nonzero feedback on specific measurements is essential for guaranteeing stability.