Yes, all of the white glues are fine for your lace.
The theory is that you build up enough glue to 'sink' the lace into it, so it disappears.
So in theory, the thinner the lace, the less glue you should need.
Mr Burns gave you a good list of white glues and its (unfortunately) a question of trying them all until you find the right one for you and the bond you want.
There is also Ghostbond & Ghostbond XL.

A lot of people have had a longer bond result using a combination of ORWG and the clear glue, Davlyn Black.