  We propose a new integrable generalization of the Toda lattice wherein the
original Flaschka-Manakov variables are coupled to newly introduced dependent
variables; the general case wherein the additional dependent variables are
vector-valued is considered. This generalization admits a Lax pair based on an
extension of the Jacobi operator, an infinite number of conservation laws and,
in a special case, a simple Hamiltonian structure. In fact, the second flow of
this generalized Toda hierarchy reduces to the usual Toda lattice when the
additional dependent variables vanish; the first flow of the hierarchy reduces
to a long wave-short wave interaction model, known as the Yajima-Oikawa system,
in a suitable continuous limit. This integrable discretization of the
Yajima-Oikawa system is essentially different from the discrete Yajima-Oikawa
system proposed in arXiv:1509.06996 (also see
https://link.aps.org/doi/10.1103/PhysRevE.91.062902) and studied in
arXiv:1804.10224. Two integrable discretizations of the nonlinear Schr\"odinger
hierarchy, the Ablowitz-Ladik hierarchy and the Konopelchenko-Chudnovsky
hierarchy, are contained in the generalized Toda hierarchy as special cases.
