Short-period double white dwarf (DWD) binaries will be the most prolific source of gravitational waves (GWs) for the Laser Interferometer Space Antenna (LISA). Not only will tens of thousands of DWDs be individually resolved, but DWDs with GW frequencies below ∼ 1 mHz will be the dominant contributor to a stochastic foreground caused by confusion from overlapping GW signals, limiting the detectability of individual sources of all kinds. Population modeling of Galactic DWDs typically assumes a standard binary fraction of 50%. However, recent observations have shown that the binary fraction of close (P orb ≤ 10 4 days) solar-type stars exhibits a strong anti-correlation with metallicity. In this study we perform the first simulation of the Galactic DWD population observable by LISA which incorporates an empirically-derived metallicity-dependent binary fraction. We simulate DWDs using the binary population synthesis suite COSMIC and incorporate a metallicity-dependent star formation history to create a Galactic population of short-period DWDs. We compare two models: one which assumes a metallicity-dependent binary fraction, and one with a binary fraction of 50%. We find that while metallicity impacts the evolution and intrinsic properties of our simulated DWD progenitor binaries, the LISA-resolvable populations of the two models remain roughly indistinguishable. However, the size of the total Galactic DWD population orbiting in the LISA frequency band is reduced by more than half when accounting for a metallicity-dependent binary fraction. This effect serves to lower the confusion foreground, effectively increasing the sensitivity for detecting all types of low-frequency LISA sources. We repeat our analysis for three different assumptions for Roche-lobe overflow interactions and find the population reduction to be robust when a metallicity-dependent binary fraction is assumed.