Opheliaflora makes a good point - your girls' names do sound southern European! (Beautiful, by the way) If you want to go with a similar feel for girl #3, here are some suggestions that I think also meet your request for an old-fashioned name:
Beatrice (this one is the ultimate international traveler, with roots in Italy, France, Spain, as well as working beautifully in English)
Clementine or Clemence
Lucia (Italian) or Lucie (French)
Your daughter's names are beautiful! I think from your list Freya fits best and I love it! Some other names I would suggest are...
Marta (instead of Martha)
Gia (this is much fresher than Georgia)
Thank you all! Piera is pronounced Pierre with an a at the end. It is Italian. I lived in Italy for 3 1/2 years. She is named after my dear friend. It is is French dialect speaking area of Italy, so many of the words are French based. I love staying closer to that same sound elegant and unusual. I love Marta too. I have a great aunt Marta. My husband knocked out both Marta and Violet too. Nona Frances is also named after a great aunt and I loved the name. I am still leaning toward a name that doesn't end in an "a". I think it may sound like I am trying to match the end sound of their names. I want it to still be elegant, unusual, and an actual name( not a made up name). It feels almost impossible. I am sure that when I hear it, it will just stick out and fit. Thank you all and I would love to hear more suggestions if any come to mind.
I also like Alice and Orly too. I am adding them to our list as well. Freya still stands out too even though it ends in "a".
My first thought was Ines/ Inez or Anais.
My favorite from you list is Anna.
Nona, Piera and
(Sorry it's quite hard to avoid the a ending)
I really like Genevieve, Bronwyn, Gissele, or Mallory. Think I am adding those too the list.
I don't really like any off your list I know you said you were leaning away from a name ending in a but my grandmas name was Vera and think it goes well with your daughters names. My favorite old lady name is Dorothy but I don't think it goes with your other names at all.
I like Vera. I think I'll add it too. We have some thinking to do... there are so many choices that after a while it is kinda overwhelming. My first two girls were so easy to name. I knew pretty much right away what to name them. I like Odette too. I need to narrow it down, choose one and figure out a middle name. Blaaaa! I really wish I knew already and that one name obviously stood out to us.