It's such a nice surprise to see something you haven't seen before (at least, in the embroidery department :-) I found these images of 13th century lace/embroidery while I was browsing through the book Seven centuries of lace by Maria Margaret Pollen (1908). You can download or browse the book for free here. The site allows you to zoom really well, so it's better to view these images from the site itself.
For those of you who are interested in smocking: the armpits in the Alb attributed to st Francis(third picture) appear to be have been smocked in a way similar to those of the Alb of St Hugo. Chris Laning, thanks for uploading this picture, and the picture of your wonderful reproduction. ! Additional note: Chris just pointed out that the reproduction was made by her friend and that it's not smocking as such but a technique called ""Italian shirring."
This type of ecclesiastical clothing always makes me wonder: Would this type of embroidery have been used in secular clothing, and if so, how, when..? I would love to know more about this!