Although the existing autonomous driving systems (ADS) can implement lane-change behaviors without human operation, they still rely on the lane-change decisions made by human drivers in a complex traffic environment. The reason is that human drivers can reasonably estimate the driving intentions of surrounding vehicles in advance, and decide their own driving trajectory according to their driving experiences. Therefore, the future ADS needs to learn the ability of human beings to predict the driving intentions of surrounding vehicles. Alternatively, it needs to make safer lane-change decisions than human beings without sacrificing the possibility as much as possible. This article develops a Lane-Change Responsibility-Sensitive Safety (LC-RSS) model to improve the safety of lane-change decisions and solve the above research gap. A novel lane-change trajectory planning method is proposed, which considers multiple interactions between the ego vehicle and surrounding vehicles with realistic position constraints and fuel consumption optimization. Specifically, it combines the lane-change prediction of surrounding vehicles to provide a more reasonable recommended lane-change trajectory for the ego vehicle, therefore, could enhance the safety constraints from the Responsibility-Sensitive Safety (RSS) model introduced in the latest published 2846-2022-IEEE Standard. The simulation results have shown that by considering lane-changing prediction in the trajectory planning module, LC-RSS not only enhances the safety of a single vehicle's recommended trajectory but also increases the traffic flow speed of the urban transportation system.