We present high-quality ALMA Band 8 observations of the [CI] $^3P_1$-$^3P_0$ line and 609 $mu$m dust continuum emission toward the nearby luminous infrared galaxy (LIRG) IRAS F18293-3413, as well as matched resolution (300-pc scale) Band 3 CO $J=$1-0 data, which allow us to assess the use of the [CI] $^3P_1$-$^3P_0$ line as a total gas mass estimator. We find that the [CI] line basically traces structures detected in CO (and dust), and a mean (median) [CI]/CO luminosity ($L_{rm [CI]}$/$L_{rm CO}$) ratio of 0.17 (0.16) with a scatter of 0.04. However, a pixel-by-pixel comparison revealed that there is a radial $L_{rm [CI]}$/$L_{rm CO}$ gradient and a superlinear $L_{rm CO}$ vs. $L_{rm [CI]}$ relation (slope = 1.54 $pm$ 0.02) at this spatial scale, which can be explained by radial excitation and/or line opacity gradients. Based on the molecular gas masses converted from the dust continuum emission, we found that the CO-to-H$_2$ and [CI]-to-H$_2$ conversion factors are relatively flat across the molecular gas disk with a median value of 3.5$^{+1.9}_{-1.3}$ and 20.7$^{+9.2}_{-4.9}$ $M_{odot}$ (K km s$^{-1}$ pc$^2$)$^{-1}$, respectively. A non-LTE calculation yields that typical molecular gas properties seen in nearby (U)LIRGs ($n_{rm H_2}$ = 10$^{3-4}$ cm$^{-3}$, $T_{rm kin}$ $sim$ 50 K, and $X_{rm CI}$ = (0.8-2.3) $times$ 10$^{-5}$) can naturally reproduce the derived [CI]-to-H$_2$ conversion factor. However, we caution that a careful treatment of the physical gas properties is required in order to measure H$_2$ gas mass distributions in galaxies using a single [CI] line. Otherwise, a single [CI] line is not a good molecular gas estimator in a spatially resolved manner.
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