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We investigate X-ray binary (XRB) luminosity function (XLF) scaling relations for Chandra detected populations of low-mass XRBs (LMXBs) within the footprints of 24 early-type galaxies. Our sample includes Chandra and HST observed galaxies at D < 25 Mpc that have estimates of the globular cluster (GC) specific frequency (SN) reported in the literature. As such, we are able to directly classify X-ray-detected sources as being either coincident with unrelated background/foreground objects, GCs, or sources that are within the fields of the galaxy targets. We model the GC and field LMXB population XLFs for all galaxies separately, and then construct global models characterizing how the LMXB XLFs vary with galaxy stellar mass and SN. We find that our field LMXB XLF models require a component that scales with SN, and has a shape consistent with that found for the GC LMXB XLF. We take this to indicate that GCs are "seeding" the galactic field LMXB population, through the ejection of GC-LMXBs and/or the diffusion of the GCs in the galactic fields themselves. However, we also find that an important LMXB XLF component is required for all galaxies that scales with stellar mass, implying that a substantial population of LMXBs are formed "in situ," which dominates the LMXB population emission for galaxies with SN < 2. For the first time, we provide a framework quantifying how directly-associated GC LMXBs, GC-seeded LMXBs, and in-situ LMXBs contribute to LMXB XLFs in the broader early-type galaxy population., Accepted for publication in ApJS. Data products and catalogs available at https://lehmer.uark.edu/downloads/