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We present Magellan/IMACS and Magellan/MIKE spectroscopy of the ultra-faint dwarf (UFD) galaxy Pictor~II (Pic~II) that is located only 12 kpc from the Large Magellanic Cloud (LMC). From the IMACS spectroscopy, we identify 13 member stars and measure a mean heliocentric velocity of , a velocity dispersion of , a mean metallicity of , and an upper limit on the metallicity dispersion of . We measure detailed elemental abundances for the brightest star, finding $\text{[Fe/H]}=-3.3$, high [ $\alpha$/Fe] ratios, and no detectable neutron capture elements, similar to stars in other UFDs. However, this star has an unusually high [Sc/Fe] ratio. The dynamical mass-to-light ratio ( $M/L={760}_{-420}^{+910}{M}_{\odot }{L}_{\odot }^{-1}$), size, and chemical abundances confirms that Pic~II is a dark matter-dominated dwarf galaxy. We perform detailed orbit modeling of Pic~II in a combined Milky Way (MW) and LMC potential and find that Pic~II is highly likely to be a long-term LMC satellite. Furthermore, we find that Pic II is likely still bound to the LMC today. Pic~II is the seventh LMC-associated UFD and among the most metal-poor UFDs known. We further update the morphological parameters with deeper Dark Energy Camera (DECam) photometry, compute the dark matter properties for dark matter indirect detection searches, verify the extremely low metallicity with narrowband CaHK imaging, and briefly discuss tidal influences of the LMC and MW.