I just sent an inquiry. It sounds as though the museum is not really in operation other than in the form of traveling exhibits. Please feel free to send your own inquiry and let us know if you hear anything. The website is http://nmcal.org/ for the National Museum of Catholic Art.
You may want to join the tatting group because that is where the Tatted Last Supper is being discussed.
As a lace historian, myself, my theory is that if you want to find lace, you look to the female relatives in a line of descent from the lacemaker, especially the sentimental ones who don't live in apartments. Did Lucy have daughters or grand-daughters, or perhaps a devoted niece? Apart from that, perhaps her church might have been the recipient of the piece? Or perhaps a religious based society? Or the local historical society or small museum? If you know where she lived in Queens you might be able to narrow it down.
One issue that occurs to me is that a big piece like that would be difficult to store adequately, and if not properly stored, it could have deteriorated after 60 years.