I'm betting it's gumpaste.. fondant would break too much. You would use a clay gun like this one
and take the resulting strings and carefully weave it through the holes..
I think that the sugarveil would be flatter on one side.. it doesn't hold it's shape when piped onto something to dry out before you can handle it.. unless you piped it and hung it off of something, but I think it would break off before you got a long enough piece.
The lace just looks like fondant or gumpaste cut out with a lace cutter and then use a round tip to make the holes for the cording to go through.