In this study, some relations between the generalized Ricci solitons with generalized quasi-Einstein manifolds and twisted products are established. Then, an explicit example of generalized quasi-Einstein spacetime endowed with the spatially homogeneous and anisotropic Bianchi type-V metric is constructed. Also, we get certain identities about the Riemannian and the Ricci tensors on a Lorentzian twisted product (M = I x(f) F,g) admitting a timelike torqued vector field. We proved that such spacetime admitting a timelike torqued vector field having a closed torqued form is a generalized Robertson- Walker spacetime. Therefore, from Mantica and Molinari's classifications, this spacetime becomes a model of perfect fluids. As a physical application, it is shown that the magnetic parts of the Weyl tensor of such spacetime vanish and so its possible Petrov types are I , D or O.