Hmmmm.....depending on the size/thickness of lanyard you want, and depending on the sizes/thicknesses of laces you could find, I almost wonder of boot laces might work. Also, Hobby Lobby or similar craft store will carry leather lace in a spool, which would work even better than boot laces, now that I think about it. Lol. Just thought of it as I was typing the first part......
I'd go with a four stand braid, which can be tricky to figure out, but looks REALLY good once you get it finished. It makes a round braid instead of a flatter braid like a three stand.