  We process the Fermi LAT data on GRB130427A using the Fermi Science Tools,
and we summarize some of the key facts that render this observation truly
remarkable, especially concerning the quality of information on high-energy
emission by GRBs. We then exploit this richness for a search of spectral lags,
of the type that has been recently of interest for its relevance in
quantum-spacetime research. We do find some evidence of systematic soft
spectral lags: when confining the analysis to photons of energies greater than
5 GeV there is an early hard development of minibursts within this long burst.
The effect turns out to be well characterized quantitatively by a linear
dependence, within such a miniburst, of the detection time on energy. With the
guidance of our findings for GRB130427A we can then recognize that some support
for these features is noticeable also in earlier Fermi-LAT GRBs, particularly
for the presence of hard minibursts whose onset is marked by the highest-energy
photon observed for the GRB. A comparison of these features for GRBs at
different redshifts provides some encouragement for a redshift dependence of
the effects of the type expected for a quantum-spacetime interpretation, but
other aspects of the analysis appear to invite the interpretation as intrinsic
properties of GRBs.

High Energy Astrophysical Phenomena;General Relativity and Quantum Cosmology