Lateral stability is a remarkably critical metric for the autonomous ground vehicle (AGV), and its loss is probable to cause a fatal accident. Various vehicular sensors, which play a key role in the lateral stability system, are coordinated to monitor the AGV's driving states. However, sensor attacks will inevitably push the AGV's lateral stability system into a insecure situation. In this paper, therefore, we investigate the security and insecurity conditions of the AGV under sensor attacks. Firstly, the dynamics output control protocol and the anomaly detector are developed in the lateral stability system. Then, we analyze the stealthiness of sensor attacks from the given detector's viewpoint. To describe how much the AGV is influenced by sensor attacks, we propose an equivalence condition associated with state variations. Besides, it is shown that internal states of the dynamics lateral controller are immune to stealthy sensor attacks. Secondly, we give a necessary and sufficient condition about the insecurity of AGV, which also motivates us how to design parameters to ensure cyber-security. Finally, we give a simulation to demonstrate the feasibility of the presented methodology. Specifically, we design a self-generated stealthy attack sequence, in which this sequence does not involve utilizing the system data in real-time.