Remarks on $tau$-functions for the difference Painleve equations of type $E_8$

We investigate the structure of $tau$-functions for the elliptic difference Painleve equation of type $E_8$. Introducing the notion of ORG $tau$-functions for the $E_8$ lattice, we construct some particular solutions which are expressed in terms of elliptic hypergeometric integrals. Also, we discuss how this construction is related to the framework of lattice $tau$-functions associated with the configuration of generic nine points in the projective plane.