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η-Ricci solitons on Lorentzian -β Kenmotsu manifold are considered an manifolds satisfying certain curvature Conditions, R(,X).S=0, S(,X).R=0, =0,.=0 We proved that in Lorentzian -Kenmotsu manifold (). Then the existence of an -Ricci solitons implies that M is Einstein manifold and if the Ricci curvature tensor satisfies, S(,X).R=0, then Ricci solitons M is steady. If the condition =0, then =0, which shows that is steady.

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