A flexible management strategy for dedicated lanes of connected and automated vehicles (CAVs) is proposed to ensure CAVs priority while enhancing overall road traffic flow when the market penetration rate (MPR) of CAVs is relatively low. A mathematical model for the flexible management strategy is constructed under a multi-lane scenario, incorporating parameters such as CAV market penetration rate, queue intensity, driving style, and road traffic demand. Numerical analysis is conducted to evaluate traffic flow under different lane management strategies across multiple scenarios, comparing the proposed flexible strategy with a typical mandatory management strategy. The analysis also considers the coexistence of human-driven vehicles (HDVs) with varying driving styles in non-dedicated lanes. Numerical results indicate that when a one-way two-lane road is configured with the inner lane as a dedicated CAV lane, 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%. As traffic demand increases from 2000 veh/h to 5000 veh/h, 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 yields similar results to the two-lane scenario. Further extending the study to a four-lane scenario, both one and two dedicated lane configurations are examined, leading to four dedicated lane management schemes. Overall, the flexible management strategy remains superior to the mandatory strategy under low and medium penetration rates. Furthermore, simulations based on SUMO in a three-lane scenario validate the effectiveness of the proposed lane management strategies.