A fluid delivery system for an inverted electric submersible pump (ESP), where the ESP has a motor section positioned above a pump section in a production path of a hydrocarbon well. The system has a supply of fluid connected to the motor section of the ESP by a supply line and a positive displacement pump that pumps fluid through the supply line to the ESP. A valve is connected between the positive displacement pump and the ESP. The valve is in an open state when the positive displacement pump is pumping fluid. A bypass line is connected in parallel to the positive displacement pump and connected between the normally closed valve and the supply of fluid, the bypass line having a check valve that permits the flow of fluid from the supply of fluid to the ESP.