We introduce a class of submanifolds, namely, Generalized Cauchy-Riemann (GCR) lightlike submanifolds of indefinite Kaehler manifolds. We show that this new class is an umbrella of invariant (complex), screen real  and CR lightlike  submanifolds. We study the existence (or non-existence) of this new class in an indefinite space form. Then, we prove characterization theorems on the existence of totally umbilical, irrotational screen real, complex and CR minimal lightlike submanifolds. We also give one example each of a non totally geodesic proper minimal GCR and CR lightlike submanifolds.