I haven’t seen or felt the yarn you’re working with so it’s impossible for me to give you a definitive answer. But, in my experience, if the yarn is marketed as yarn… lace weight or not, it should be perfectly fine to knit with one strand for a lace shawl. That’s what it’s MADE for.
If this particular yarn you have is so fragile that it won’t even hold up to knitting, then it’s best suited as a pretty skein in your yarn basket. But, I’m telling you, if it’s yarn, then you can use it as yarn. And knit with it. Single, double, OR triple stranded… whatever you want to do with it.