The fast, epitaxial deposition of Pb films on Cu(100) was monitored by helium atom beam scattering over the substrate temperature range of 150-400 K. A growth mode transition from Stranski-Krastanov to quasi-layer-by-layer growth was observed by decreasing the deposition temperature. From 150 to 180 K, intensity oscillations of the specularly reflected helium beam show a complex modulated pattern which is interpreted as due to the concurrent influence of transition in growth mode and structure and of quantum size effects in the overlayer electronic states. From low-energy electron diffraction observations, it was found that Pb grows along [111] direction with two domains rotated 90-degrees with respect to each other at temperatures from 150 to 218 K.