The rapid development of connected and autonomous vehicle (CAV) technology and the outperformance of the managed lane have drawn increasing attention with respect to wonder whether the CAV operating in the managed lane is helpful. Therefore, this study focuses on the methodology applied to explore whether the managed lane is beneficial in the gradual application of CAVs. Three managed lanes are considered, namely a bus lane, CAV dedicated lane, and high-occupancy vehicle lane. Given the unfamiliarity with the travel mode related to CAVs, the attitudinal variables for CAVs and their influencing relationship are designed and quantified by a structural equation model based on the extended technology acceptance model. A two-level nested logit model with different types of managed lanes as explanatory variables is further developed to analyze the travel choice of traditional modes and CAV modes. The difference in probabilities of travel choices under managed lanes is also explored. The results indicate that the three managed lanes have a positive influence on promoting the adoption of the CAV modes, with an increase of at least 13.5% shifted from traditional modes in the conventional lane. Moreover, the influences of managed lanes differ between transit CAVs and non-transit CAVs. The probabilities of choosing transit CAVs under three managed lanes increase in the range of 12.9%–27.2%, while those of non-transit CAVs only show a maximum 6.5% increase in the CAV dedicated lane. The study is expected to assist in designing differentiated development of CAVs with the deployment of managed lanes.