If they're to the point of disintergrating when you touch them, they may be dry rotted beyond restoration.. If no one on this list comes up with ideas, try contacting your local museum or historical society..

If structural & not historical integrity is your goal, you can possibly.. possibly line the garments with tricot fusible interfacing.. it's what I used as a conservator at a costume house that specializes in vintage & antique garments for principal players in major motion pictures.. the caveats being:

1) you have to be sure eveything is on straight grain, both the textile and the tricot, or it looks like crap.
2) be sure you really really want to do this.. there's no real going back once you've commited to this process, and like taking the finish off an antique piece of furniture, this stabilization will decrease the value for some collectors.
3) There's not guarantee a garment stabilized this way will be 100% wearable.. it will still be fragile.

sounds like your best bet is display.. controlled humidity, UV glass, no air, etc.

If there are any salvageable patches.. you can use them on newer garments & have bits of your ancestry still wearable, if not the entire thing...

Maybe you could take cuts of them and sandwich them between glass for either a wall hanging or floating piece (think room divider, stained glass alternative)?

I don't know if its possible, but maybe you could make molds of them and convert the lace pattern into a different medium?

Or send it to a place like this:
www.gownsremembered.com/services.html

If just the lace is disintegrating and the rest of the garment is holding together you could try replacing the lace itself. I did that with a shirt that I put in the dryer too long and destroyed the lace and it came out rather well.