An effective transportation system is part of the core of a modern smart city to support various human activities. Recent developments of Connected Autonomous Vehicles (CAVs) have great impact on the automotive industry. Due to its numerous advantages, CAV is expected to get popular in the near future. While most studies focus on standalone CAV technologies, there is much potential on collective CAV control. With the connectivity and automation of CAVs, we can employ Dynamic Lane Reversal (DLR) to enable automatic lane reversal for improving the traffic. We can optimize the travel schedules of CAVs based on DLR for performance enhancement. In this paper, we proposed the Dynamic Lane Reversal-Traffic Scheduling Management (DLR- TSM) Scheme for CAVs. It collects the travel requests from the CAVs and determines their optimal schedules and routes on dynamically reversible lanes. We formulate the routing and scheduling problem as an integer linear program. We evaluate the performance of the scheme with real-world transportation data. The simulation results show that DLR-TSM can significantly improve the travel times of CAVs.