A neutron lifetime measurement conducted at the Japan Proton Accelerator Research Complex (J-PARC) is counting the number of electrons from neutron decays with a time projection chamber (TPC). The $gamma$ rays produced in the TPC cause irreducible background events. To achieve the precise measurement, the inner walls of the TPC consist of $^6$Li-enriched lithium-fluoride ($^6$LiF) tiles to suppress the amount of $gamma$ rays. In order to estimate the amount of $gamma$ rays from the $^{6}{rm LiF}$ tile, prompt gamma ray analysis (PGA) measurements were performed using germanium detectors. We reconstructed the measured $gamma$-ray energy spectrum using a Monte Carlo simulation with the stripping method. Comparing the measured spectrum with a simulated one, the number of $gamma$ rays emitted from the$^{6}{rm LiF}$ tile was $(2.3^{+0.7}_{-0.3}) times 10^{-4}$ per incident neutron. This is $1.4^{+0.5}_{-0.2}$ times the value assumed for a mole fraction of the $^{6}{rm LiF}$ tile. We concluded that the amount of $gamma$ rays produced from the $^{6}{rm LiF}$ tile is not more twice the originally assumed value.
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