In this paper, we present an adaptive and predictive control framework which improves the lateral stability and the tracking performance of an autonomous vehicle operating in various road conditions. We particularly focus on the modeling errors caused by simplifications while deriving a steering model employed in predictive controller. Such simplifications could degrade the control performance. In order to enhance the prediction accuracy, we propose to use a data-driven model of the steering system where the parameters are identified online by a recursive least squares algorithm. The proposed model is simple~(no mathematical derivation) and does not depend on tire forces which is usually approximated by linear models. We first validate the system identification algorithm by applying a test signal sequence to the steering actuator of our test vehicle. Then, the performance of the proposed control framework is evaluated in simulations where we compare the results of two predictive control frameworks in a automated lane change scenario with different road conditions. The simulation results show the effectiveness of the proposed method in handling the modeling mismatch and the control performance is improved under various road conditions.