In this paper, we investigate the geometric characterizations of 3-dimensional Lorentzian trans-Sasakian manifolds admitting a generalized Z-tensor. First, we analyze the behavior of the generalized Z-tensor under certain symmetry conditions, such as Codazzi type, cyclic parallel, and -Z symmetric conditions, and derive the necessary constraints on the manifold structure. We also study the existence of generalized Z-Ricci solitons and prove that the existence of such a soliton implies that the scalar curvature is constant and the soliton generally exhibits a shrinking behavior.
Zeren et al. (Wed,) studied this question.