I've worked a bit with vintage clothing, In NC I worked at The Costume Shoppe for 7 years and we were always getting donated "grandma's attic" stuff.
When lace is really old, to the disintigrating point, there really isnt much you can do at that point other than put it in a glass case and admire what was. If the stuff seems to be holding up,though, you can always wear it. Keep an eye on the seams, as thread will disentigrate before the rest of the fabric often times. . Avoid washing machines (duh) and harsh detergents. Bady odor will stain old clothes really easily too.
I hope this helps a little.

I would suggest getting it away from any plastic right away. Ask your local dry cleaner what they would use to store, say, a wedding dress as far as wrapping. I've heard of wrapping heirloom quilts and things into clean cotton sheets. The goal is to get the old fabric away from heat and moisture fluctuations while still allowing it to breathe. A quilt shop might also know.
If you want to wear it, you might try backing it with something (sheer maybe) so that the lace can be shown without being called upon for structural integrity.
My only other suggestion to keep it from breaking down any further is if you sweat on the garment, spray those ares with vodka (can be the cheap stuff put in a spray bottle) and allow to dry before storing. Vodka kills smelly and stainy bacteria and flash dries, so no worries about mildew.
Good luck. Would love to see some pictures.... ;)

For reference, these are two textile restorers:

West Coast:
-- Textile Repair Studio, 1625 Shattuck Ave., Suite 312, Berkeley. (510) 548-2267. www.quiltrepair.com
www.sfgate.com/cgi-bin/article.cgi

East Coast:
Costume & Textile Specialists
Colleen Callahan: (Richmond, VA area) 804.261.4998 (phone/fax)
Newbie Richardson: (metro Washington, DC area) 703.684.0863 (phone/fax)
www.costumeandtextile.net/Index.html

Anyone able to list more?