What a treasure. I have a lot of crocheted lace -- much of it from the early 1900's - and I wash it with no problem. The thing to remember about crocheted lace is that it can draw up when washed and needs to be blocked so stitching it down would help it keep its shape.
Another thing-- I would be concerned about the buttons pulling on the lace. When my grandmother made her lace (I have table cloths, bedspreads, doilies, etc) she did not knot when she ran out of one skein and started a new one -- she overlapped the ends. If your lace is not knotted, the stress of the buttons could cause the lace to come apart (Having DH lay on top of one of my bedspreads caused it to start to come apart -- it was a pain to fix.)