Abstract <p>This paper delves into the realm of 4-dimensional Lorentzian Walker manifolds, focusing on the study of Riemann solitons within this context. The primary objective is to conduct a comprehensive classification of all Riemann solitons on 4-dimensional Lorentzian Walker manifolds and to ascertain the specific characteristics of potential vector fields associated with Riemann solitons, including the identification of the Killing vector field, Ricci collineation vector field, and the potential vector field of Ricci solitons.</p>