  In this work, we consider a generalization of quantum electrodynamics
including Lorentz violation and torsional-gravity, in the context of general
spinor fields as classified in the Lounesto scheme. Singular spinor fields will
be shown to be less sensitive to the Lorentz violation, as far as couplings
between the spinor bilinear covariants and torsion are regarded. In addition,
we prove that flagpole spinor fields do not admit minimal coupling to the
torsion. In general, mass dimension four couplings are deeply affected when
singular flagpole spinors are considered, instead of the usual Dirac spinors.
We also construct a mapping between spinors in the covariant framework and
spinors in Lorentz symmetry breaking scenarios, showing how one may
transliterate spinors of different classes between the two cases. Specific
examples concerning the mapping of Dirac spinor fields in Lorentz violating
scenarios into flagpole and flag-dipole spinors with full Lorentz invariance
(including the cases of Weyl and Majorana spinors) are worked out.
