The q-analogue of probability distributions provides a framework that offers a broader range of definitions for them and also includes their classical forms. This paper introduces the q-analogue of a new one-parameter generalized lifetime distribution and thoroughly examines its distributional and statistical characteristics. The study includes modeling the q-analogues of the probability density function and cumulative distribution function, along with an exploration of their shapes through rigorous mathematical analysis. Moreover, the q-analogues of moments and related measures are derived for the proposed q-distribution. Furthermore, the q-analogues of the reliability functions, central moment, and moment generating function for non-negative q-continuous random variables are defined and presented for the proposed q-distribution. In addition, this paper presents the Lindley q-distribution derived from the proposed q-distribution, comparing its q-distributional properties with those of the classical form. Finally, this paper focuses on estimating the parameters of the proposed q-distribution. While the method of moments is commonly used for continuous q-distributions due to their complexity, discrepancies occur between empirical and theoretical q-moments as q deviates from 1. To address this, we propose a modified method for calculating empirical q-moments, ensuring consistency and reliability even for small q values.