In this paper we prove that there do not exist warped product $GCR$-lightlike submanifolds in the form $M=N_{\bot}\times_{\lambda}N_T$ such that $N_{\bot}$ is an anti-invariant submanifold tangent to $V$ and $N_T$ an invariant submanifold of $\overline{M}$, other than $GCR$-lightlike product in an indefinite cosymplectic manifold. We also obtain some characterizations for a $GCR$-lightlike submanifold to be locally a $GCR$-lightlike warped product.