  This contribution sets out to pursue the investigation of a supersymmetric
electrodynamics model with Lorentz-symmetry violation (LSV) manifested by a
space-time unbalance in the propagation of the fermionic charged matter.
Despite violation of Lorentz symmetry, the supersymmetry algebra is kept
untouched. We then adopt a superspace approach to build up an
$\mathcal{N}=1$-supersymmetric Abelian gauge theory in presence of a
Lorentz-violating background supermultiplet that accommodates the space-time
asymmetry parameter of the charged matter. We describe, in this scenario, how
the particular Lorentz-symmetry breaking, brought about by the fermionic
matter, affects its (matter) scalar partners and the photon/photino that
minimally couple to charged matter. From the (modified) Dirac, Klein-Gordon and
Maxwell field equations, we work out the corresponding dispersion relations to
inspect and discuss the physical effects of the LSV Majorana fermion
condensates that naturally emerge from the background supermultiplet. Finally,
we target efforts to investigate the Gordon decomposition of the charged lepton
electromagnetic current. This is carried out by iterating the (fermion and
scalar) matter field equations, which points to an effective contribution to
the electron's electric dipole moment (EDM). This result allows us to attain an
estimate of the pseudo-vector condensate of the (LSV) Majorana background
fermion.
