Interestingly, Lucy and Roxy are similar in meaning - both mean "light" (Roxy also means "dawn").
I know you don't want an "L" name but the first name that popped in my head when I saw her pic was "LuLu". I went and looked that meaning up just to see what it was and it is: "precious; pearl; calm; peaceful; protected"
I think you should just get to know her and her personality and the right name will come to you
