Looking at mine now (from Roden Gray), single flex welt sole for sure. As for lined or not, I'm not sure. The heel part has a leather lining but the front does not. Does this mean they're unlined? For your research, the model number on the box is 29331F.
Velomane, thank you for the info, that helps a lot. Can you confirm that the shoe is on the Barrie last?