We used oxide molecular-beam epitaxy in a composition-spread geometry to deposit hexagonal LuFeO3 (h-LuFeO3) thin films with a monotonic variation in the Lu/Fe cation ratio, creating a mosaic of samples that ranged from iron rich to lutetium rich. We characterized the effects of composition variation with x-ray diffraction, atomic force microscopy, scanning transmission electron microscopy, and superconducting quantum interference device magnetometry. After identifying growth conditions leading to stoichiometric film growth, an additional sample was grown with a rotating sample stage. From this stoichiometric sample, we determined stoichiometric h-LuFeO3 to have a TN = 147 K and Ms = 0.018 μB/Fe.