Generalized Robertson-Walker (GRW) spacetime is the generalization of the Robertson-Walker (RW) spacetime and a further generalization of GRW spacetime is the twisted spacetime. In this paper, we generalize the results of the paper [C. A. Mantica, Y. J. Suh and U. C. De, A note on generalized Robertson-Walker spacetimes, Int. J. Geom. Methods Mod. Phys. 13 (2016), Article Id: 1650079, 9 pp., doi:101142/s0219887816500791]. We prove that a Ricci simple Lorentzian manifold with vanishing quasi-conformal curvature tensor is a RW spacetime. Further, we prove that a Ricci simple Lorentzian manifold with harmonic quasi-conformal curvature tensor is a GRW spacetime. As a consequence, we obtain several corollaries. Finally, we have cited some examples of the obtained results. © 2019 World Scientific Publishing Company.