  Light axion-like particles (ALPs) are expected to be abundantly produced in
core-collapse supernovae (CCSNe), resulting in a $\sim$10-second long burst of
ALPs. These particles subsequently undergo conversion into gamma-rays in
external magnetic fields to produce a long gamma-ray burst (GRB) with a
characteristic spectrum peaking in the 30--100-MeV energy range. At the same
time, CCSNe are invoked as progenitors of {\it ordinary} long GRBs, rendering
it relevant to conduct a comprehensive search for ALP spectral signatures using
the observations of long GRB with the \textit{Fermi} Large Area Telescope
(LAT). We perform a data-driven sensitivity analysis to determine CCSN
distances for which a detection of an ALP signal is possible with the LAT's
low-energy (LLE) technique which, in contrast to the standard LAT analysis,
allows for a a larger effective area for energies down to 30~MeV. Assuming an
ALP mass $m_a \lesssim 10^{-10}$~eV and ALP-photon coupling $g_{a\gamma} =
5.3\times 10^{-12}$ GeV$^{-1}$, values considered and deduced in ALP searches
from SN1987A, we find that the distance limit ranges from $\sim\!0.5$ to
$\sim\!10$~Mpc, depending on the sky location and the CCSN progenitor mass.
Furthermore, we select a candidate sample of twenty-four GRBs and carry out a
model comparison analysis in which we consider different GRB spectral models
with and without an ALP signal component. We find that the inclusion of an ALP
contribution does not result in any statistically significant improvement of
the fits to the data. We discuss the statistical method used in our analysis
and the underlying physical assumptions, the feasibility of setting upper
limits on the ALP-photon coupling, and give an outlook on future telescopes in
the context of ALP searches.
