I found this fabulous pattern in a book called Torchon lacemaking, a manuel of techniques by Elizabeth Wade. There are a number of other gorgeous patterns in this book so I highly recommend it, at least to a relative novice to bobbin lace like myself. The thread I used was DMC 100 and I interpreted the fans in three different ways; half stitch, whole stitch and whole stitch with an extra stitch between each row. My favourite is the half stitch doily. Here's how it looked before I mounted it onto fabric.
To mount them onto fabric I cut circles that were about a quarter of an inch bigger than I wanted. I then used a single needle overlock stitch on my overlocker to ensure that the edges would not fray. I then sewed the bobbin lace to the circles, turning the overlocked edges to the underside so that they were hidden. I did not use the tradition end pin stitch to attach them, I used a regular running stitch as I did not want to create more bulk. Here are the finished items.
In the lower image the half stitch Doily is on the left, the whole stitch doily at the bottom and the whole stitch doily with the extra twist between the rows is on the right. I am now working on a lavender bag, how very vintage!