Ginerva (I prefer this alternative spelling/pronunciation to
Ginevra)
GenevaGeorginaRegina
Lucille is different enough from
Lucia for cousins. It isn't as if they are siblings, but if it seems like an issue, you could always use it as a middle name.
Lucinda is a nice alternative.
Names with nature meanings:
Aria - "air"
Marin - "of the sea"
Silva- "forest"
Stella- "star"
Avani - "earth"
Mira- "sea, ocean"
Holly- "holy tree"
Laurel- "victory"