The X-ray-illuminated surface of the accretion disk in a low-mass X-ray Binary (LMXRB) and the X-ray-heated corona above the disk produce optical, UV, and soft X-ray emission lines. This paper presents one-dimensional models of the emission line spectra and the vertical temperature and density structures at different radii. The models include a detailed treatment of the important atomic processes and an escape probability treatment of radiative transfer. A companion paper (Soker & Raymond) uses the density structure predicted by these models for a two-dimensional Monte Carlo simulation of the photon scattering in the accretion disk corona (ADC) to examine the effects of the ADC on the angular distribution of X-rays and the flux of X-rays incident on the outer disk. This paper concentrates on the emission line fluxes for various elemental abundances and disk parameters. The UV lines of the classic LMXRBs are consistent with the model predictions. Some CNO processing is necessary to account for the nitrogen and helium abundances in Sco X-1 and other LMXRBs. Comparison of the models with observed spectra also points to a soft X-ray component with luminosity comparable to the hard X-rays. The models predict a substantial luminosity in the group of highly ionized iron lines near 100 angstrom. They also predict a significant zone where cooling by atomic processes dominates Compton heating and cooling, and the temperature is a fraction of the Compton temperature.