We present theoretical models for populations of low-mass X-ray binaries in two elliptical galaxies NGC3379 and NGC4278. The models are calculated with the recently updated StarTrack code , and are targeted to modeling and understanding the origin of the X-ray luminosity functions (XLF) in these galaxies. For the first time we explore the population XLF down to luminosities of 3×1036ergs-1, as probed by the most recent observational results . We consider models for the formation and evolution of low-mass X-ray binaries (LMXB) in galactic fields with different common envelope efficiencies, stellar wind prescriptions and initial mass functions. We identify models that produce an XLF in excellent agreement with the observations both in shape and number of systems at a specific luminosity. We also find that the treatment of the outburst luminosity of transient systems remains a crucial parameter for the determination of the XLF as the modeled populations are dominated by transient X-ray systems. Finally, we propose a physically motivated and self-consistent prescription for the modeling of transient neutron star (NS) LMXB properties, such as duty cycle (DC), outburst duration and recurrence time. We compare the transient LMXB population to the Chandra X-ray survey of the two elliptical galaxies NGC3379 and NGC4278, which revealed several transient sources [3, 4]. Our comparison suggests that transient LMXBs are very rare in globular clusters (GC), and thus the number of identified transient LMXBs may be used as a tracer of the relative contribution of field and GC LMXB populations.