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Supersymmetric lattice Ward-Takahashi identities are investigatedperturbatively up to two-loop corrections for super doubler approach of $N=2$lattice Wess-Zumino models in 1- and 2-dimensions. In this approach notoriouschiral fermion doublers are treated as physical particles and momentumconservation 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 weconfirm that exact supersymmetry on the lattice is realized for allsupercharges at the quantum level. Delicate issues of associativity are alsodiscussed.

Exact Lattice Supersymmetry at the Quantum Level for $N=2$ Wess-Zumino Models in 1- and 2-Dimensions