Increasing attention is being paid to intersection signal control with cooperative platoons. Assuming platoons being formed, such platoons cannot only improve the intersection capacity but also minimize the number of control units, especially when dedicated connected and automated vehicle (CAV) lanes are considered. However, the platoon formation process is often neglected, especially for lane-changing and overtaking maneuvers in mixed traffic. This may jeopardize the potential of signal control with platoons. This article proposes a platoon formation algorithm that computes the optimal lane, platoon sequence, and speed profiles of CAVs under the requirement of the central traffic controller. The algorithm is designed for mixed traffic conditions and hence the performance of human-driven vehicles is also considered. A mixed integer linear program model is formulated to minimize the deviation from the desired platoon configuration and the disturbance to overall traffic under any arbitrary initial condition. Numerical experiments are designed to test the effectiveness and the computational performance of the proposed algorithm. Results show that CAVs with signal control can form platoons with rational motion. Besides, the platoon penetration significantly affects platooning feasibility, while the platoon length does not. This suggests that CAVs can form long platoons at intersections to improve traffic throughput.