The advanced controls of Connected Autonomous Vehicles (CAVs) have enabled complex traffic management for higher efficiency and safety, such as dynamic lane assignment and non-signalized autonomous intersection management (AIM). Unlike traditional intersections, non-signalized AIM does not rely on the settings of signal phases or traffic-light cycles for controlling the traffic, and the measurements of lane congestion can no longer be based on these two settings. Moreover, in the CAV environment, lane use can be more dynamic in response to real-time traffic demands and the policy of AIM. Therefore, we proposed a new AIM system (named Roadrunner) that combines dynamic lane assignment and autonomous intersection management. In Roadrunner, lane use is not limited by turns, and lanes are dynamically assigned to CAVs, based on our lane-assignment policy and a novel approach of measuring lane congestion levels over non-signalized intersection controls. We implemented Roadrunner in a SUMO simulator and compared the performance with different intersection management systems, where lane use is predefined. The result shows that Roadrunner increases the intersection capacity by more than 11%, and CAVs have lower average traveling delay.