J'aime Lillian!!! It's so beautiful! I do go for more uncommon names, but I just adore Lillian and have to have it on my list.
I'm not fond of Avery on a girl, though.
Can I make suggestions?
Lillian Ava
Lillian Claire
Lillian Charlotte
Lillian Rosalie [a bit Twilight, but pretty nonetheless]
Lillian Cassandra
Lillian Aimée
Lillian Julia
Lillian Maria
Lillian Caroline
Lillian Aslý [an uncommon Turkish name, pronounced AZ-la. Sorry if the 'y' with accent comes up, it should be Asli without a dot over the 'i'.]