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 LATs 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 $g_{agamma} = 5.3times 10^{-12}$ 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.
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