I don't think you should care to much about what other berries say. It's your daughter, whatever name feels right is probably right.
Adalia/Adelia/Adeliah are beautiful and Lydia is a personal favourite.
How about Adelia Katherine Lydia? or (I don't know what other name options you've got...) Personally, I love the Adelia spelling the most. Adelia Jennifer Lydia? I think as long you put a name between Adelia-Lydia, you're fine. I saw some other people suggested Adele. i don't think it's nearly as pretty, but Adele Lydia works, so if you change your mind about the double name, that's always an option. And Addie is absolutely adorable! Good luck!
Thanks for your help! It gives me more options and I feel I can use both names and not stick them together so awkwardly. Will play with the name a little more and will poll again whenever I come up with something I like. I do like some of the suggestions that have been given. I think they flow better than I previously thought as long as there is another name with it.