In this paper, we propose a new class of distributions called the Lindley generator with one extra parameter to generate many continuous distributions. The new distribution contains several distributions as sub-models, such as Lindley-Exponential, Lindley-Weibull, and Lindley-Lomax. Some mathematical properties of the new generator, including ordinary moments, quantile and generating functions, limiting behaviors, some entropy measures and order statistics, which hold for any baseline model, are presented. Then, we discuss the maximum likelihood method to estimate model parameters. The importance of the new generator is illustrated by means of three real data sets. Applications show that the new family of distributions can provide a better fit than several existing lifetime models.