Q. Dear Donia,
A. Dear Kat,
What a wonderful item to have to remember your great-grandmother!
Starching is not the best for older fabrics as we just don't know what is in our modern starches, spray, liquid or otherwise. Especially dangerous would be weeing and pinning, especially if you don't know how the original materials have aged. What you could consider is having your framer gently stitch the points onto the underlying mat board with a thread that blends with the crochet and is chemically stable (polyester is good here). It shouldn't be tied too tightly that it could cut through the original fibers but just enough to hold it in place. I have done this for a couple of christening gowns I have framed. It works really well and is very easy to remove if needed.