  In this article, by means of using discrete zero curvature representation and
constructing opportune time evolution problems, two new discrete integrable
lattice hierarchies with n-dependent coefficients are proposed, which related
to a new discrete Schr\"{o}dinger nonisospectral operator equation. The
relation of the two new lattice hierarchies with the Volterra hierarchy is
discussed. It has been shown that one lattice hierarchy is equivalent to the
positive Volterra hierarchy with n-dependent coefficients and another lattice
hierarchy with isospectral problem is equivalent to the negative Volterra
hierarchy. We demonstrate the existence of infinitely many conservation laws
for the two lattice hierarchies and give the corresponding conserved densities
and the associated fluxes formulaically. Thus their integrability is confirmed.
