this post a kind reader named Betty (no blog) wrote me and confirmed the bobbin lace and the hairpin lace. She is very knowledgeable and I so appreciate her help!
The piece on the right is a mystery. This is the second one I have found and I sold the first one in my Etsy last Spring. My MIL is pretty knowledgeable about handwork but her specialty is knitting and crochet. All she could tell me about this technique is she thinks it is worked over ribbon. I haven't been able to spot anything similar in my new books. Can any of you tell me anything about it?
Now about that confession... I am an authentic doily geek. I USE them. Always have. Always will. Yep, there, I said it. My easy chair even wears the exact same arm covers and anti-Madagascar that my mother used before me.