  We investigate an integrable property and observables of 2 dimensional
N=(4,4) topological field theory defined on a discrete lattice by using the
"orbifolding" and "deconstruction" methods. We show that our lattice model
possesses the integrability and the partition function reduces to matrix
integrals of scalar fields on sites in consequence. We make clear meaningful
differences between the discrete lattice and differentiable manifold, which
would be important to a study of topological quantities on the lattice. We also
propose a new construction of N=(2,2) supersymmetric lattice theory, which is
realized by a suitable truncation of scalar fields from the N=(4,4) theory.
