I agree, my favorite is Lady!
Adelaide is one of my favorite names and it's really so versatile because of its many nickname options. I have to agree, I always thought Lady was darling! I'm not a fan of Addy since it's so popular. My favorite has to be Ada. I think it's just so charming and sophisticated and vintage sounding. Adele and Della are two other favorite options that both give me the same feel as Ada.
My daughter is Adelaide also, only part of the reason I chose that name is because I love "Addie" as a nickname (and I have for about 15 years, when it was relatively unheard of!). I realize it is very popular now due to Addison, but we still call her Addie most of the time. Her other nickname is "Ladie", which I think is so cute too!