High-resolution infrared spectra of comet C/2014 Q2 Lovejoy were acquired with NIRSPEC at the W. M. Keck Observatory on two post-perihelion dates (UT 2015 February 2 and 3). H2O was measured simultaneously with CO, CH3OH, H2CO, CH4, C2H6, C2H4, C2H2, HCN, and NH3 on both dates, and rotational temperatures, production rates, relative abundances, H2O ortho-to-para ratios, and spatial distributions in the coma were determined. The first detection of C2H4 in a comet from ground-based observations is reported. Abundances relative to H2O for all species were found to be in the typical range compared with values for other comets in the overall population to date. There is evidence of variability in rotational temperatures and production rates on timescales that are small compared with the rotational period of the comet. Spatial distributions of volatiles in the coma suggest complex outgassing behavior. CH3OH, HCN, C2H6, and CH4 spatial distributions in the coma are consistent with direct release from associated ices in the nucleus and are peaked in a more sunward direction compared with co-measured dust. H2O spatial profiles are clearly distinct from these other four species, likely due to a sizable coma contribution from icy grain sublimation. Spatial distributions for C2H2, H2CO, and NH3 suggest substantial contributions from extended coma sources, providing further evidence for distinct origins and associations for these species in comets. CO shows a different spatial distribution compared with other volatiles, consistent with jet activity from discrete nucleus ice sources.