On some integrable lattice related by the Miura-type transformation to the Itoh-Narita-Bogoyavlenskii lattice

We show that by Miura-type transformation the Itoh-Narita-Bogoyavlenskii lattice, for any $n\ge 1$, is related to some differential-difference (modified) equation. We present corresponding integrable hierarchies in its explicit form. We study the elementary Darboux transformation for modified equations.