A Li-rich red giant (RG) star (2M19411367+4003382) recently discovered in the direction of NGC 6819 belongs to the rare subset of Li-rich stars that have not yet evolved to the luminosity bump, an evolutionary stage where models predict Li can be replenished. The currently favored model to explain Li enhancement in first-ascent RGs like 2M19411367+4003382 requires deep mixing into the stellar interior. Testing this model requires a measurement of 12C/13C, which is possible to obtain from Apache Point Observatory Galactic Evolution Experiment (APOGEE) spectra. However, the Li-rich star also has abnormal asteroseismic properties that call into question its membership in the cluster, even though its radial velocity and location on color–magnitude diagrams are consistent with membership. To address these puzzles, we have measured a wide array of abundances in the Li-rich star and three comparison stars using spectra taken as part of the APOGEE survey to determine the degree of stellar mixing, address the question of membership, and measure the surface gravity. We confirm that the Li-rich star is a RG with the same overall chemistry as the other cluster giants. However, its log g is significantly lower, consistent with the asteroseismology results and suggestive of a very low mass if the star is indeed a cluster member. Regardless of the cluster membership, the 12C/13C and C/N ratios of the Li-rich star are consistent with standard first dredge-up, indicating that Li dilution has already occurred, and inconsistent with internal Li enrichment scenarios that require deep mixing.