During a winter thunderstorm on November 24, 2017, a downward terrestrial gamma-ray flash took place and triggered photonuclear reactions with atmospheric nitrogen and oxygen nuclei, coincident with a lightning discharge at the Kashiwazaki-Kariwa nuclear power station in Japan. We directly detected neutrons produced by the photonuclear reactions with gadolinium orthosilicate scintillation crystals installed at sea level. Two gadolinium isotopes included in the scintillation crystals, $^{155}$Gd and $^{157}$Gd, have large cross-sections of neutron captures to thermal neutrons such as $^{155}$Gd(n,$gamma$)$^{156}$Gd and $^{157}$Gd(n,$gamma$)$^{158}$Gd. De-excitation gamma rays from $^{156}$Gd and $^{158}$Gd are self-absorbed in the scintillation crystals, and make spectral-line features which can be distinguished from other non-neutron signals. The neutron burst lasted for $sim$100~ms, and neutron fluences are estimated to be $>$52 and $>$31~neutrons~cm$^{-2}$ at two observation points inside the power plant. Gadolinium orthosilicate scintillators work as valid detectors for thermal neutrons in lightning.
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