We study the emission from H-like ions, particularly oxygen and neon, observed in ASCA spectra of low-mass X-ray binaries (LMXBs). The observed strengths of Ly alpha emission lines relative to the recombination continua differ from the classical recombination model. This suggests a different excitation mechanism for the lines. Various mechanisms are considered, which include three-body recombination, collisional excitation, recombination satellite line emission, and resonant fluorescent excitation. We find that the detection of Lyman recombination continuum implies that the plasma is photoionized, in agreement with previous studies by Hatchett, Buff, & McCray and Liedahl & Paerels. Under collisional ionization conditions, on the other hand, the Lyman continuum should be negligible unless the temperature were greater than 3 x 10(6) K. Otherwise, the enhancement of Ly alpha emission with respect to the continuum may be due to (1) three-body recombination at electron densities greater than 10(17) cm(-3) and temperatures below 2 x 10(5) K, (2) contributions to the recombination spectrum from collisional excitation of the H-like ionization stage, (3) contributions to recombination Ly alpha emission from satellite lines due to recombination onto the He-like ionization stage, and (4) contributions to the recombination spectrum from resonant fluorescence excitation of the H-like ionization stage. Further observations of higher order Lyman series lines and lines from other ionization stages are suggested to discriminate between the various excitation mechanisms. In addition, the implications of the different spectral formation mechanisms to the hydrodynamic accretion model of LMXBs are discussed.