  The Rashba superconductor, in which spin-splitting bands become
superconducting, is fascinating as a novel superconducting system in low
dimensional systems. Here, we present the results of $\textit{in-situ}$
transport measurements on a Rashba-type surface state of the striped
incommensurate (SIC) phase of a Pb atomic layer on Ge(111) surface with
additional Pb islands/clusters on it. We found that two-step superconducting
transitions at around 7 K and 3 K occurred. The latter superconducting
transition is suggested to be induced at the non-superconducting Rashba SIC
area because of the lateral proximity effect caused by the superconducting Pb
clusters. Our results propose a new type of Rashba superconductor, which is a
new platform to understand the Rashba superconducting systems.
