If they are family names then it's a double winner.
I would hesitate over Beatrice usually but's that's the anti-monarchist in me coming out. Call her the Italian one, it will really only be in your family that people use it, and they will all say it right. It gives her some cache having an unusaul name. And something to resent you for when she's a teenager. That's very important.
Lily is a really pretty name, and has no behavioural/learning problems attached to it. I would have no concerns when reading that name on the class roll. Very good name.
Reassure your husband teasing over names is passe now. Nobody will blink at Lily - and kids don't start using their second names for some years. They are usually fascinated to find they have one. She will be quite safe. (I think it's safeto say that children where you are have the same basic nature as here.)
When is she due? This is so nice.