  In this work we have used a Ho\v{r}ava-Lifshitz scaling to rewrite a
Lorentz-violating higher-order derivative electrodynamics controlled by a
background four-vector $n_{\mu}$. The photon propagator was obtained and we
have analyzed the dispersion relation and the observational results of
gamma-ray burst (GRB) experiments were used. The limits of the critical
exponent were discussed in the light of the GRB data and the physical
implications were compared with the current GRB-Lorentz-invariance-violation
literature. We show that the bound for the Lorentz-violating coupling for
dimension-six operators, obtained from a Ho\v{r}ava-Lifshitz scaling, is eight
orders of magnitude better than the result found without considering a
Ho\v{r}ava-Lifshitz scaling, also this bound is nearby one, which is expected
to be relevant phenomenologically.
