In this paper, we investigate lightlike hypersurfaces which are semi-symmetric, Ricci semi-syminetric, parallel or semi-parallel in a semi-Euclidean space. We obtain that every screen conformal lightlike hypersurface of the Minkowski spacetime is semi-symmetric. For higher dimensions, we show that the semi-symmetry condition of a, screen conformal lightlike hypersurface reduces to the semi-symmetry condition of a leaf of its screen distribution. We also obtain that semi-symmetric and Ricci semi-symmetric lightlike hypersurfaces are totally geodesic under certain conditions. Moreover, we show that there exist no non-totally geodesic parallel hypersurfaces in a Lorentzian space.