We model the ultraviolet spectra of the Seyfert 1 galaxy NGC 5548 obtained with the Hubble Space Telescope during the 6 month reverberation mapping campaign in 2014. Our model of the emission from NGC 5548 corrects for overlying absorption and deblends the individual emission lines. Using the modeled spectra, we measure the response to continuum variations for the deblended and absorption-corrected individual broad emission lines, the velocity-dependent profiles of Lyα and C IV, and the narrow and broad intrinsic absorption features. We find that the time lags for the corrected emission lines are comparable to those for the original data. The velocity-binned lag profiles of Lyα and C IV have a double-peaked structure indicative of a truncated Keplerian disk. The narrow absorption lines show a delayed response to continuum variations corresponding to recombination in gas with a density of ∼105 cm‑3. The high-ionization narrow absorption lines decorrelate from continuum variations during the same period as the broad emission lines. Analyzing the response of these absorption lines during this period shows that the ionizing flux is diminished in strength relative to the far-ultraviolet continuum. The broad absorption lines associated with the X-ray obscurer decrease in strength during this same time interval. The appearance of X-ray obscuration in ∼2012 corresponds with an increase in the luminosity of NGC 5548 following an extended low state. We suggest that the obscurer is a disk wind triggered by the brightening of NGC 5548 following the decrease in size of the broad-line region during the preceding low-luminosity state.