<p>The chemostat is a key experimental apparatus for investigating microbial growth and population dynamics, while the predator-prey model serves as a classic theoretical framework for analyzing interspecific interactions in ecology. To gain a deeper understanding of ecosystem dynamics, stability and long-term behavior, in this study, we focus on a predator-prey chemostat model with the log-normal Ornstein-Uhlenbeck (OU) process. The biological rationale for the log-normal OU process is its alignment with two critical biological constraints: strict non-negativity of key variables and regulated stochasticity via natural feedbacks. Its log-normal transformation ensures positivity, and OU mean-reversion captures homeostatic regulation, enabling biologically realistic stochastic modeling. We firstly demonstrate the existence, uniqueness and global nature of positive solution through constructing appropriate Lyapunov functions. Secondly, a set of threshold conditions is offered to describe long-term behavior of the model, which determines persistence and extinction of predator and prey. Moreover, using the finite independent superposition principle, matrix similarity transformation and Routh-Hurwitz criterion, we provide a detailed form of the density function near the positive equilibrium point of corresponding deterministic model. Ultimately, several numerical simulations are used to reinforce theoretical results.</p>