I call my sister Lilliana even though it's not her name! And she calls me Uplyana. Er... makes sense in context.
I prefer
Lillian.
Liliana seems too elaborate. I also can only think of my sister and it's a jokey nn so that puts it further into the negative column.
Lillian is so pretty and I can see it on all ages. Lil is a great nickname but I also adore
Lily. I don't think
Lily is 100% unavoidable but when she's young if you remain adamant I'm sure you won't have too much trouble. And, really, if she likes to be called
Lily, after a while the name might grow on you because she'll be your lovebug daughter anyway. :)