  We show how to derive Catterall's supersymmetric lattice gauge theories
directly from the general principle of orbifolding followed by a variant of the
usual deconstruction. These theories are forced to be complexified due to a
clash between charge assignments under U(1)-symmetries and lattice assignments
in terms of scalar, vector and tensor components for the fermions. Other
prescriptions for how to discretize the theory follow automatically by
orbifolding and deconstruction. We find that Catterall's complexified model for
the two-dimensional N=(2,2) theory has two independent preserved
supersymmetries. We comment on consistent truncations to lattice theories
without this complexification and with the correct continuum limit. The
construction of lattice theories this way is general, and can be used to derive
new supersymmetric lattice theories through the orbifolding procedure. As an
example, we apply the prescription to topologically twisted four-dimensional
N=2 supersymmetric Yang-Mills theory. We show that a consistent truncation is
closely related to the lattice formulation previously given by Sugino.
