Abstract: The highway on-ramp merging area is a common bottleneck prone to traffic congestion and accidents. With the current trajectory and advancements in automotive technology, intelligent vehicle infrastructure cooperative control based on connected and automated vehicles (CAVs) is a fundamental solution to this problem. While much existing research focuses solely on ramp merging control in single-lane highway scenarios, there is more than one main lane in the actual highway environment. Thus, this paper proposes a dual-clutch longitudinal-lateral cooperative planning model, inspired by the principle of dual-clutch transmission, to address this gap. Besides, considering the impact of communication delay on control effects within the internet of vehicles, the paper proposes a system delay prediction model, which integrates the adaptive Kalman filter algorithm, the elitist non-dominated sorting genetic algorithm based on imitation learning, and the radial basis function neural network. The delay predicted dual-clutch on-ramp merging control model (DPDM) applied to two-lane highways for CAVs makes up of these two models above. Then, the performance of the DPDM is analyzed under different traffic densities on two-lane highways through simulation. The findings underscore the DPDM's pronounced comprehensive advantages in enhancing group vehicle safety, expediting and stabilizing merging processes, optimizing traffic flow speed, and economizing fuel consumption.