I can vouch for Dharma Trading Company (http://www.dharmatrading.com) since I use them frequently. They are perhaps the best resource in America for Procion Mix Dyes (the type of dye to use for natural fibers like cotton, linen, etc).
I also wanted to comment that the article suggests washing the lace with 'soapy water' - I suggest you use Synthrapol for dying water-based lace.
Also, if you dye on paper towels, the towels can transfer or spread the dye. Use an empty picture frame and pin the lace so it is elevated off the table. This will keep the dye from spreading. In addition, many dyes require 'fixing' in order to stabilize the dye in the fabric. These processes were not clearly described in this article. Use a good dye book for better results.