  The efforts in this contribution consist in reassessing a modified Dirac
equation that incorporates a $\gamma^0 \gamma_5$-Lorentz-symmetry violating
(LSV) term induced as a Loop Quantum Gravity (LQG) effect. Originally, this
equation has been applied and considered as a good scenario for describing a
number of investigations on the flight time of cosmic photons and neutrinos,
which suggests that the speed of light in vacuum, in connection with the
geometry that describes a granular space-time, takes an energy-dependent form,
e.g., $v(E) =1 \pm E/E_{\tiny{\textrm{LSV}}}$, with $E_{\tiny{\textrm{LSV}}}
\approx 6,5 \times 10^{17}$ GeV for neutrinos. Once LQG provides a viable way
to consistently understand this picture, we pursue an analysis of this
effective Dirac equation to inspect some of its properties. These include: the
derivation of the modified fermionic propagator, attainment of the Gordon
decomposition of the vector current with minimal electromagnetic coupling to
obtain information on the form factors, examination of the non-relativistic
limit of the equation, evaluation of the spin- and velocity-dependent
corrections to the Coulomb potential due to LQG effects, and the modified
Hamiltonian in the low-relativistic regime. The study of the form factors may
open up paths to set up bounds on the LQG parameters from the precision
measurements of electromagnetic attributes of the charged leptons, such as
their respective electric and magnetic dipole moments.
