  We investigate the structure of $\tau$-functions for the elliptic difference
Painlev\'e 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.
