Teleoperation is increasingly being adopted as a critical fallback for autonomous vehicles. However, the impact of network latency on vision-based, perception-driven control remains insufficiently studied. The present work investigates the nonlinear degradation of closed-loop stability in camera-based lane keeping under varying network delays. To conduct this study, we developed the Latency-Aware Vision Teleoperation testbed (LAVT), a research-oriented ROS 2 framework that enables precise, distributed one-way latency measurement and reproducible delay injection. Using LAVT, we performed 180 closed-loop experiments in simulation across diverse road geometries. Our findings reveal a sharp collapse in stability between 150 ms and 225 ms of one-way perception latency, where route completion rates drop from 100% to below 50% as oscillatory instability and phase-lag effects emerge. We further demonstrate that additional control-channel delay compounds these effects, significantly accelerating system failure even under constant visual latency. By combining this systematic empirical characterization with the LAVT testbed, this work provides quantitative insights into perception-driven instability and establishes a reproducible baseline for future latency-compensation and predictive control strategies. Project page, supplementary video, and code are available at https://bimilab.github.io/paper-LAVT