The collision avoidance system in an autonomous vehicle, intended to address traffic safety issues, has a crucial function called collision estimation. It accomplishes this by identifying potential dangers and notifying the drivers in advance or by using autonomous control to navigate safely. In this work, a novel approach is proposed for generating and selecting a lane-change trajectory for the vehicle in a driving scenario where two vehicles are simultaneously executing lane-change processes on highways and approaching the same target lane. Moreover, a novel fuzzy logic estimator based on time-to-collision (TTC) and time-to-gap (TTG) is designed to estimate the collision risk. In the collision-avoidance process, the proposed estimator is utilized to determine the risk of a collision with polynomial function-based generation of possible lane-change trajectories. The safest lane-change trajectory is then provided to the motion controller so it can navigate the vehicle safely through such a challenging lane-change scenario. This work also investigates Stanley and Pure Pursuit controllers to follow the optimized trajectory. The simulation experiment results demonstrate that the proposed approach for dynamic trajectory generation during the lane-change process can successfully handle this type of challenging situation and prevent a potential collision. Experimental results also indicate that monitoring the movement of the nearby lane-changing vehicle is crucial for safe lane-change execution and that the proposed approach successfully handles the challenging situation, preventing potential collision.