  Supersymmetric lattice Ward-Takahashi identities are investigated
perturbatively up to two-loop corrections for super doubler approach of $N=2$
lattice Wess-Zumino models in 1- and 2-dimensions. In this approach notorious
chiral fermion doublers are treated as physical particles and momentum
conservation is modified in such a way that lattice Leibniz rule is satisfied.
The two major difficulties to keep exact lattice supersymmetry are overcome.
This formulation defines, however, nonlocal field theory. Nevertheless we
confirm that exact supersymmetry on the lattice is realized for all
supercharges at the quantum level. Delicate issues of associativity are also
discussed.
