To address the common neglect of longitudinal–lateral coupling effects in conventional vehicle platoon control studies, this paper proposes a five-degree-of-freedom dynamics–Magic Formula–lane-keeping integrated model suitable for commercial vehicle platoon control. The model is linearized to construct a linear time-varying system, based on which a model predictive controller is designed. To validate the effectiveness of the proposed approach, co-simulation experiments are conducted in Matlab/Simulink and TruckSim. The results show that, the proposed method achieves superior real-time performance while maintaining control accuracy, providing a practical technical solution for the engineering application of commercial truck platoons.