In the present paper, we set out to examine warped product lightlike submanifolds of semi-Riemannian product manifolds. Significantly, considering the warped product GCR-lightlike submanifolds of the type N⊥ ×λ NT and NT ×λ N⊥, we obtain their non-existence in a semi-Riemannian product manifold N, where NT and N⊥, respectively, denotes a holomorphic submanifold and a totally real submanifold of N.