Accelerated Life Test has been introduced as a tool to aid in obtaining sufficient failure time data of test units quickly and extrapolating lifetime information under use conditions. When the lifetime of units is distributed by the Lindley model, the estimations for the unknown parameters and the reliability function are established based on two frequentist methods and Bayesian method of estimation using Type-II censored data under constant-stress accelerated life test. In the frequentist methods, besides, the conventional likelihood-based estimation, another competitive method, known as the maximum product of spacing method is proposed for estimating the parameters and the reliability function under normal conditions as an alternative approach to the common likelihood method. In Bayesian estimation, both maximum likelihood and maximum product of spacing-based Bayesian estimates are discussed for unknown parameters as well as the reliability function. Moreover, the approximate confidence intervals and highest posterior density credible intervals of the parameters and reliability function are also obtained. Extensive Monte-Carlo simulation studies are conducted to evaluate the performance of the proposed estimates. Finally, to demonstrate the proposed methodology, two real-life accelerated life test data are considered to show the applicabilities of the proposed methods.