In the baseline design of the International Linear Collider (ILC) an undulator-based source is foreseen for the positron source in order to match the physics requirements. The recently chosen first energy stage with sqrt(s)=250 GeV requires high luminosity and imposes an effort for all positron source designs at high-energy colliders. In this paper we perform a simulation study and adopt the new technology of plasma lenses to capture the positrons generated by the undulator photons and to create the required high luminosity positron beam.