This paper presents the first UV (1400-3200 Angstrom) polarimetry and far-UV (950-1200 Angstrom) spectrophotometry ever obtained for reddened stars in the Large Magellanic Cloud (LMC). We derive the UV wavelength dependence of interstellar polarization down to 1400 Angstrom and that of extinction down to near the Lyman limit. We also measure column densities of H-2 along these lines of sight in the LMC. We have obtained these data with the Hopkins Ultraviolet Telescope (HUT) and the Wisconsin Ultraviolet Photo-Polarimeter Experiment (WUPPE) using the Astro-2 Observatory, which hew on the Space Shuttle in 1995 March. The UV interstellar polarization in the LMC shows a wavelength dependence similar to that seen in the Galaxy. The magnitude of the polarization in the UV lies on or above an extrapolation of the Serkowski curve. This is consistent with the wavelength dependence seen for low lambda(max) sight lines in the Galaxy. The far-UV extinction in the LMC continues to rise to 10.5 mu m(-1), which confirms that large numbers of small grains are present. The measured column densities of H-2 with respect to H I are low compared to the Galaxy and track the previously measured lower dust abundance. The H-2 abundance may be regulated by the amount of dust present. These new data will allow a comparison of how interstellar dust properties vary in different galactic environments.