  We consider a stochastic lattice Cahn-Hilliard equation with nonautonomous
nonlinear noise. First, we prove the existence of pullback random attractors in
$\ell^2$ for the generated nonautonomous random dynamical system. Then, we
construct the time-dependent invariant sample Borel probability measures based
on the pullback random attractor. Moreover, we develop a general stochastic
Liouville type equation for nonautonomous random dynamical systems and show
that the invariant sample measures obtained satisfy the stochastic Liouville
type equation. At last, we define a new kind of statistical solution -- sample
statistical solution corresponding to the invariant sample measures and show
that each family of invariant sample measures is a sample statistical solution.
