The maturing intelligent connected autonomous driving technology presents a novel solution to the increasing traffic congestion and energy wastage issues at the signalized intersection. Integrating traffic signal control with vehicle trajectory optimization holds significant promise in enhancing traffic throughput and fuel efficiency. Therefore, addressing the multi-lane signalized intersection in mixed traffic flow environments, this paper proposes an integrated optimization framework for traffic signal and vehicle trajectory. Initially, improvements are made to the longitudinal car-following model and lateral lane-change model, considering the dynamic changes in signal sequencing and the reasons behind vehicle lane-changing, as well as the persistent impact of vehicle lane-changing processes. Subsequently, an integrated optimization method is established with the goal of minimizing vehicle travel delays and fuel consumption, which achieves adaptive traffic signal control and smooth vehicle trajectory. Furthermore, an integrated optimization control algorithm is devised to ensure minimal computational overhead while guaranteeing optimizing efficiency. Finally, numerical simulations conducted in various traffic scenarios indicate that the proposed framework significantly improves both traffic throughput and fuel efficiency. Compared to individual optimization frameworks for traffic signal or vehicle trajectory, the proposed framework demonstrates notable additional benefits in terms of travel delay, fuel consumption, safety performance and driving comfort.