Make, learn and talk about needle lace.
I prefer linen for bobbin lace and I have also used it for needlelace. Linen is just a tad hairy and varies in thickness slightly along its length, and I like both of those characteristics. I say this because many lacemakers don't like those aspects of linen. I have used 40/2 linen by HV GARN (no longer manufactured) and Fawcetts. Fresia 40/2 would be comparable. I have also used 20/2 Fawcett's linen. There are several companies now selling 16/2 as weaving linen, and it is a little hairier than the 20/2 but slightly softer.
My leaf 10 was worked in 20/2 linen and these 2 were worked in 40/2 linen
green leaf and pink flower
One real advantage to linen is that it doesn't stretch and the hairiness will keep your stitches where you put them. I think 16/2 weaving linen could be used for large scale work. If you want finer go with the same manufacturers that bobbin lacers use: Bockens and Fresia. Moravia is another.
I checked the catalogue of the Cooper-Hewitt and their Krejci piece is actually bobbin lace. But the piece that has been attached, Luba's horsewoman, is said to be "nitak" something the artist invented herself. There is another Krejci piece, in the Powerhouse museum, described as knotted and needlewoven. It is made out of sisal. I have no idea how she produces these works or what nitak is. I will be interested to see your work.
... I have a catalogue for an exhibition La Dentelle tcheque: de L'Art Deco a nos jours. It was from an exhibition at the Brussels Royal Museum of Art and History in 1983. It has some large 2 D and 3 D hangings. In fact, one of them is by Luba Krejci. It is called Helios. Hmm. Intereting co-incidence that, since we are all to try to make a sun themed piece of needlelace. It says it is a technique derived from Needlelace. I don't know if the International Old Lacers would have this catalogue in its lending library or not.