In the present paper, we study the quasi-Yamabe solitons and almost quasi-Yamabe solitons on the lightlike hypersurfaces of the semi-Riemannian manifolds endowed with a torse-forming vector field. We show some conditions for the lightlike hypersurfaces to be quasi-Yamabe solitons and almost quasi- Yamabe solitons with the tangential component of the torse-forming vector field on the semi-Riemannian manifolds as the soliton field. In particular, we also specify the conditions for lightlike hypersurfaces of (n + 2)-dimension semi-Riemannian manifolds of constant curvature to be quasi-Yamabe solitons and almost quasi-Yamabe solitons. Besides, we provide some geometric properties of the lightlike hypersurfaces satisfying quasi-Yamabe solitons, quasi-Yamabe gradient solitons, almost quasi-Yamabe solitons and almost quasi-Yamabe gradient solitons. Furthermore, we investigate properties of screen homothetic lightlike hypersurfaces admitting quasi-Yamabe solitons and almost quasi-Yamabe solitons.