We show that the orbital variation in the UV P Cygni lines of the X-ray binary LMC X-4 results when X-rays photoionize nearly the entire region outside of the X-ray shadow of the normal star . We fit models to Goddard High Resolution Spectrograph ( GHRS ) observations of \ion N5 and \ion C4 P Cygni line profiles . Analytic methods assuming a spherically symmetric wind show that the wind velocity law is well-fit by v \propto ( 1 - 1 / r ) ^ { \beta } , where \beta is likely \approx 1.4 - 1.6 and definitely < 2.5 . Escape probability models can fit the observed P Cygni profiles , and provide measurements of the stellar wind parameters . The fits determine L _ { x } / \dot { M } = 2.6 \pm 0.1 \times 10 ^ { 43 } erg s ^ { -1 } \mbox { M } _ { \odot } ^ { -1 } yr , where L _ { x } is the X-ray luminosity and \dot { M } is the mass-loss rate of the star . Allowing an inhomogeneous wind improves the fits . IUE spectra show greater P Cygni absorption during the second half of the orbit than during the first . We discuss possible causes of this effect .