We studied electrical transport through a Pb monolayer on Ge(111), which has a metallic surface state with a large Rashba spin splitting. The Pb monolayer was found to be metallic down to 9 K. The macroscopic sheet conductivity was 10.2 +/- 1.0mS/square at 9K, which is much higher than those of other metallic monolayers. We found that the microscopic step conductivity is two orders of magnitude larger than those in other metallic monolayers, being the main cause of the high macroscopic conductivity. The transport electron-phonon (e-ph) coupling constant obtained by a temperature-dependent conductance measurement is 0.16 +/- 0.03, indicating weak e-ph coupling compared to bulk Pb (1.1-1.5). This result is supported by temperature-dependent angle-resolved photoelectron spectroscopy.