We introduce a prioritized system-optimal algorithm for mandatory lane change (MLC) behavior of connected and automated vehicles (CAV) from a dedicated lane. Our approach applies a cooperative lane change that prioritizes the decisions of lane changing vehicles which are closer to the end of the diverging zone (DZ), and optimizes the predicted total system travel time. Our experiments on synthetic data show that the proposed algorithm improves the traffic network efficiency by attaining higher speeds in the dedicated lane and earlier MLC positions while ensuring a low computational time. Our approach outperforms the traditional gap acceptance model.