We introduce the study of a new class of a lightlike submer-sion ϕ : K₁ → K′ from a screen generic lightlike submanifold of an indef-inite Kaehler manifold K₂ onto an indefinite almost Hermitian manifold K′, and show that for this case K′ must be an indefinite Kaehler man-ifold. Then, we derive a relationship between the holomorphic sectional curvatures of K₂ and K′. Finally, we present a classification theorem for a screen generic lightlike submersion, giving the relationship between the sectional curvatures of the total space K₂ and the fibers.