We have carried out an in-depth study of low-mass X-ray binaries (LMXBs) detected in the nearby lenticular galaxy NGC 3115, using the Megasecond Chandra X-Ray Visionary Project observation (total exposure time 1.1 Ms). In total we found 136 candidate LMXBs in the field and 49 in globular clusters (GCs) above 2sigma detection, with 0.3--8 keV luminosity L_X ~10^36-10^39 erg/s. Other than 13 transient candidates, the sources overall have less long-term variability at higher luminosity, at least at L_X > 2x10^37 erg/s. In order to identify the nature and spectral state of our sources, we compared their collective spectral properties based on single-component models (a simple power law or a multicolor disk) with the spectral evolution seen in representative Galactic LMXBs. We found that in the L_X versus photon index Gamma_PL and L_X versus disk temperature kT_MCD plots, most of our sources fall on a narrow track in which the spectral shape hardens with increasing luminosity below L_X~7x10^37 erg/s but is relatively constant (Gamma_PL~1.5 or kT_MCD~1.5 keV) above this luminosity, similar to the spectral evolution of Galactic neutron star (NS) LMXBs in the soft state in the Chandra bandpass. Therefore we identified the track as the NS LMXB soft-state track and suggested sources with L_X<7x10^37 erg/s as atolls in the soft state and those with L_X>7x10^37 erg/s as Z sources. Ten other sources (five are transients) displayed significantly softer spectra and are probably black hole X-ray binaries in the thermal state. One of them (persistent) is in a metal-poor GC.
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