I don't think
Lillian is common at all! But from opinions on name boards I think it might grow soon, but not for a couple of years. There are definitely more
Lillie / Lillys etc about than
Lillian nn
Lillie. Personally I prefer the look and sound of
Liliana, for me it seems less dated and more "fun".
I do however really like
Lillian, it would be nice for her to be
Lillian for the majority of the time but occasionally called
Lillie I see no problem with.