As part of the Early Science Large Millimeter Telescope projects, we report the detection of nine double-peaked molecular lines, produced by a rotating molecular torus, in the ultraluminous infrared galaxies (ULIRG) - Compton-thick active galactic nuclei (AGN) galaxy UGC 5101. The double-peaked lines we report correspond to molecular transitions of HCN, HCO+, HNC, N2H+, CS, C18O, 13CO, and two CN lines; plus the detection of C2H that is a blend of six lines. The redshift search receiver spectra covers the 73-113 GHz frequency window. Low- and high-density gas tracers of the torus have different implied rotational velocities, with a rotational velocity of 149 ± 3 km s-1 for the low-density ones (C18O, 13CO) and 174 ± 3 km s-1 for high-density tracers (HCN, HCO+, HNC, N2H+, CS, and CN). In UGC 5101, we find that the ratio of integrated intensities of HCN to 13CO to be unusually large, probably indicating that the gas in the torus is very dense. Both the column densities and abundances are consistent with values found in AGN, starburst, and ULIRG galaxies. The observed abundance ratios cannot discriminate between X-ray and UV-field-dominated regions.