Proposed in this paper is a flexible management strategy for the dedicated lanes of connected autonomous vehicles (CAVs), which is used to ensure CAVs priority while enhancing the overall road traffic flow when the market penetration rate (MPR) of CAVs is relatively low. In the investigation, first, a mathematical model for the flexible management strategy is constructed in a multi-lane scenario, incorporating parameters such as CAV market penetration rate, queue intensity, driving style and road traffic demand. Then, numerical analysis is conducted to evaluate the traffic flow under different lane management strategies in multiple scenarios, and a comparison between the proposed flexible management strategy with the typical mandatory one is performed, with the coexistence of human-driven vehicles (HDVs) with different driving styles in non-dedicated lanes being also considered. Numerical analysis results indicate that, when a one-way two-lane road is configured with the inner lane as a dedicated CAV lane, as traffic demand increases from 2000 veh/h to 5000 veh/h, the flexible management strategy consistently outperforms the mandatory strategy in terms of road traffic flow when MPR is below 50%, particularly, when MPR is below 30%, the advantage of the flexible management strategy becomes more evident, suggesting its suitability under low MPR conditions. Additionally, the flexible management strategy supports a broader MPR range to achieve the target traffic demand, with an earlier starting point of the effective MPR interval. This difference becomes more pronounced as the driving style of CAVs becomes more aggressive. However, when MPR exceeds 50%, both strategies exhibit similar traffic flow trends under identical driving styles. For a one-way three-lane scenario with the inner lane designated as a dedicated lane, the analysis results are similar to those of the two-lane scenario. Furthermore, the proposed strategy is extended to a four-lane scenario with one or two dedicated lanes, with four dedicated lane management schemes being analyzed. It is found that the flexible management strategy remains superior to the mandatory one under low and medium penetration rates. Finally, simulations based on SUMO in a one-way three-lane scenario are carried out, and the effectiveness of the proposed lane management strategies is validated.