My honest opinion is that I really don't like it. For one thing, it's a nickname for Dolores. It doesn't stand up well with your son's name- he has a full name, she would just get a nickname.
I do think of both the songs you mentioned, and the book Lolita. It has sort of a sexy/strippery feel to it that I don't like, and it seems a little bit trendy and downmarket. It just has too many negative associations.
I really like Ruby and Lucy a lot better.
Similar names that aren't nicknames and don't have any negative associations that I can think of: Lana, Lara, Leila, Lila, Lilia, Lily, Lora, Lori.
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