  We examine the N=2 Wess-Zumino model defined on the $d=2$ Euclidean lattice
in connection with a restoration of the Leibniz rule in the limit $a\to0$ in
perturbatively finite theory. We are interested in the difference between the
Wilson and Ginsparg-Wilson fermions and in the effects of extra interactions
introduced by an analysis of Nicolai mapping. As for the Wilson fermion, it
induces a linear divergence to individual tadpole diagrams in the limit
$a\to0$, which is absent in the Ginsparg-Wilson fermion. This divergence
suggests that a careful choice of lattice regularization is required in a
reliable numerical simulation. As for the effects of the extra couplings
introduced by an analysis of Nicolai mapping, the extra couplings do not
completely remedy the supersymmetry breaking in correlation functions induced
by the failure of the Leibniz rule in perturbation theory, though those
couplings ensure the vanishing of vacuum energy arising from disconnected
diagrams. Supersymmetry in correlation functions is recovered in the limit
$a\to 0$ {\em with or without} those extra couplings. In the context of lattice
theory, it may be properly said that supersymmetry does not improve ultraviolet
properties but rather it is well accommodated in theories with good ultraviolet
properties.
