Yes they are lined and this is a Kravet fabric with jute/twine in it which is trade-only. They were custom made by our drapery workroom but if you show this picture to your local fabric and drapery resource they may be able to find something similar.

It's been a while since you asked about the drapes so maybe you found something. I had this photo in an idea book for some other reason and just came back to look. Anyway, I have seen a very similar looking drape at cost plus world market to the fabric here. Of course, it's not lined and is not nearly as nice as custom is, but just thought I would throw it out there for you in case it could work for you. I had some hanging as a shower curtain for a while and they look nice. It's an interesting fabric with the texture of the twine right in it.

Here's a photo from their website.

Truffle lover - I was going to comment recommending those exact curtains from World Market, I have them in "Cress Green" and am really happy with them.