I love it. The only think about Lidia is that it looks a little short to me. Lydia is definitely a full name, but Lidia looks like it could be short for Alidia or Elidia or something like that.
Lydia is fairly narrow, it's mature/badass feminine. Lidia can do that but it can also be a little more delicate because of the i, so it fits with tougher names like Bronimira and Eleonora and also frillier names like Celestina.
I like:
Lidia Avdotya
Lidia Azucena *
Lidia Bronimira
Lidia Casimira *
Lidia Celestina
Lidia Cosmina *
Lidia Eleonora *
Lidia Elvira
Lidia Fiammetta
Lidia Fortunata
Lidia Frederica - or Federica
Lidia Ginevra
Lidia Giovanna
Lidia Lucretia -- Whenever you post these lists I immediately delete all the repeating-initial combos, but I'm willing to let the double L slide for this one!
Lidia Maristella
Lidia Maurizia
Lidia Melisande *
Lidia Merofleda *
Lidia Nevena
Lidia Polissena
Lidia Proserpina **** this one is great. I also think that the shift from Lydia to Lidia is similar to the shift from Persephone to Propserpina. They shift in opposite directions and meet in the middle. Like, if left is harder and right is sweeter, it goes like: Lydia --> Lidia Proserpina