I really like the names Lily and Anna separately and together. Anna would be after me, and Lily as a nickname , used a full name, for Elizabeth. However, I don't like the spelling Lili very much, I prefer Lily. WDYT of the spelling Lilyanna or LilyAnna (two words).
I dislike that spelling. I would spell it Liliana (i PRN it more like lily-ON-uh). She can still go by "Lily" as a NN. Or you could give her first name Lily MN Anna. I wouldn't spell it Lilyanna, it looks horribly trendy and destroys a good name.
I really like the name Anna (only as Ana, but I'm not too fond of Lilly. Although, Analilly is very cute. That's just me, though. Lilyana would be my preferedspelling.