We present high spatial resolution LBTI/NOMIC $9-12$ $mu m$ images of VY CMa and its massive outflow feature, the Southwest (SW) Clump. Combined with high-resolution imaging from HST ($0.4-1$ $mu m$) and LBT/LMIRCam ($1-5$ $mu m$), we isolate the spectral energy distribution (SED) of the clump from the star itself. Using radiative-transfer code DUSTY, we model both the scattered light from VY CMa and the thermal emission from the dust in the clump to estimate the optical depth, mass, and temperature of the SW Clump. The SW Clump is optically thick at 8.9 $mu m$ with a brightness temperature of $sim$200 K. With a dust chemistry of equal parts silicates and metallic iron, as well as assumptions on grain size distribution, we estimate a dust mass of $5.4times10^{-5},M_odot$. For a gas--to--dust ratio of 100, this implies a total mass of $5.4times10^{-3},M_odot$. Compared to the typical mass-loss rate of VY CMa, the SW Clump represents an extreme, localized mass-loss event from $lesssim300$ years ago.
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