•Highlight the power of Monte Carlo Tree Search for cooperative driving planning.•Provide a fast yet effective cooperative driving planning for autonomous vehicles.•Allow lane change of cooperative driving vehicles. This paper studies the cooperative driving of connected and automated vehicles (CAVs) at conflict areas (e.g., non-signalized intersections and ramping regions). Due to safety concerns, most existing studies prohibit lane change since this may cause lateral collisions when coordination is not appropriately performed. However, in many traffic scenarios (e.g., work zones), vehicles must change lanes. To solve this problem, we categorize the potential collision into two kinds and thus establish a bi-level planning problem. The right-of-way of vehicles for the critical conflict zone is considered in the upper-level, and the right-of-way of vehicles during lane changes is then resolved in the lower-level. The solutions of the upper-level problem are represented in tree space, and a near-optimal solution is searched for by combining Monte Carlo Tree Search (MCTS) with some heuristic rules within a very short planning time. The proposed strategy is suitable for not only the shortest delay objective but also other objectives (e.g., energy-saving). Numerical examples show that the proposed strategy leads to good traffic performance in real-time.