In this paper we study certain curvature properties of Lorentzian Para-Sasakian manifold (shortly, LPSM) with respect to the generalized symmetric metric connection. Here we discuss \(\xi\)-concircularly, \(\xi\)-conformally and \(\xi\) projectively flat \(L P S M\) with respect to the generalized symmetric metric connection and obtain various interesting results. Moreover, we study \(L P S M\) with \(\tilde{Z}(\xi, V) . \tilde{S}=0\), where \(\tilde{Z}\) and \(\tilde{S}\) are the concircular curvature tensor and Ricci tensor respectively with respect to the generalized symmetric metric connection.