If I were to have a dd named
Elizabeth, I'd call her
Ellie but only because
Bess wouldn't work with my surname.
Bess is the best, ha!
In your situation, so while I like
Ellie, there's something about
Elle that puts me off (perhaps because it seems like more of a nn for
Eleanor, I don't know). Besides,
Lily as a nick for
Elizabeth is so sweetly old fashioned that I can't resist it here.