We apply high resolution spectroscopy to investigate the lunar exosphere by measuring sodium and potassium spectral line profiles to determine the variations in exospheric effective temperatures and velocities. Observations were made at the National Solar Observatory McMath-Pierce Telescope during May 2014. Data were collected over several nights, centered on full moon (May 14) and covering a waxing phase angle of 67 to a waning phase angle of 75. We used a dual-etalon Fabry-Perot spectrometer with a resolving power of 184,000 (1.63 km s-1) to measure the line widths and radial velocity shifts of the sodium D2 (5889.951 ) and potassium D1 (7698.965 ) emission lines. The field of view was 3 arcmin (~330 km) and positioned at several locations, each centered at 1.5 arcmin (~165 km) off the East and West sunlit limbs. The deconvolved line widths indicate significant differences between the sodium and potassium temperatures. The sodium line widths were mostly symmetric as a function of phase for both the waxing and waning phases. At phase angles > 40 (outside of the magnetotail) the full width half maximum (FWHM) line widths are 1.5 2.0 km s-1 or ~1500 K for FWHM = 1.75 km s-1. Inside the magnetotail (phase angle < 40) and near full moon (phase angle ~6), the FWHM increased to ~4 km s-1. The implied line width temperature is 8000 K, although some of the observed line width may be due to a dispersion in velocities from many contribution along the extended sodium tail. Unlike sodium, the potassium line widths are wider by 50% during the waxing phase compared to the waning phase at phases > 40. The potassium temperatures pre-magnetotail passage are ~1000 K while the temperatures post-magnetotail passage are ~2000K.At phase angles < 40, the potassium intensities decreased dramatically; on consecutive days, when the phase angle changed from 44 to 31 to 20, the relative intensities dropped by 1.0:0.6:0.15.The potassium intensity in the East and West equatorial regions (latitude < 10) were similar; however, the potassium intensity was brightest off the limb near Aristarchus (latitude ~24), which was the crater we observed nearest the KREEP region.