This paper proposes a novel lane change path optimization algorithm for emergency collision avoidance in intelligent vehicles. Traditional path planning often faces challenges such as optimizing many variables, being unsuitable for emergency scenarios, or producing paths that are difficult for vehicles to follow accurately. Our approach employs lagged longitudinal and lagged curvature models with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$G^2$</tex-math></inline-formula> continuous curves, generating reliable collision avoidance trajectories under low-level actuator time lag. The lagged longitudinal model is designed to be differentiable in the spatial domain, allowing curvature optimization in the curvilinear coordinates. The lagged curvature model facilitates rapid lane changes, making it suitable for emergency collision avoidance. The proposed method optimizes only dual connecting points and enhances computational efficiency using analytic gradient-based nonlinear programming. Comparisons with existing path planning methods–namely, the fifth-order spline optimization method, model predictive control-based optimization, and the time-domain fifth-order polynomial optimization method–on straight and curved roads demonstrate that the proposed method minimizes collision avoidance areas more effectively. The proposed path is verified with a simple tracking controller in high-fidelity simulation using TruckSim.