In this paper, we study ƞ-Ricci solitons on Lorentzian para-Sasakian manifold satisfying
R(ξ,X)•W_5(Y,Z)U=0 and W_5(ξ,X)•R(Y,Z)U=0 conditions.
We prove that on a Lorentzian para-Sasakian manifold (M,ξ,ƞ,g), the Ricci curvature tensor satisfying
any one of the given conditions, the existence of ƞ-Ricci soliton then implies that (M,g) is Einstein
manifold. We also conclude that in these cases, there is no Ricci soliton on M, with the potential vector
field ξ (the killing vector).