  In this paper we study the warped product submanifolds of a Lorentzian
paracosymplectic manifold and obtain some nonexistence results. We show that a
warped product semi-invariant submanifold in the form
{$M=M_{T}\times_{f}M_{\bot}$} of Lorentzian paracosymplectic manifold such that
the characteristic vector field is normal to $M$ is an usual Riemannian product
manifold where totally geodesic and totally umbilical submanifolds of warped
product are invariant and anti-invariant, respectively. We prove that the
distributions involved in the definition of a warped product semi-invariant
submanifold are always integrable. A necessary and sufficient condition for a
semi-invariant submanifold of a Lorentzian paracosymplectic manifold to be
warped product semi-invariant submanifold is obtained. We also investigate the
existence and nonexistence of warped product semi-slant and warped product
anti-slant submanifolds in a Lorentzian paracosymplectic manifold.
