This study presents a novel investigation into the use of a window–liquid metal target configuration for x-ray generation, covering a broad electron beam energy range (100 keV - 1 MeV), using FLUKA Monte Carlo simulation. Unlike conventional solid tungsten targets, this approach explores lightweight, low-Z window materials including titanium, diamond, beryllium, and beryllia, coupled with a lead-bismuth eutectic (LBE) to enhance x-ray production. The structural design of the beam windows is carefully addressed, to ensure safe operation. The findings reveal critical energy-dependent relationships between electron transmission, x-ray yield, and thermal load management. Notably, an optimal performance is observed near 500 keV, where both electron penetration and x-ray brightness are maximized. This study provides the first in-depth evaluation of window–liquid metal target systems across this energy range, offering valuable insights for the development of new x-ray sources.