"she lives" is correct. " is a proper way to start a question, but only when it stands alone. "she does live" would only be used if you were contrasting with where she does not live.
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colorfulratioHave you any idea ... ?This set of words is followed by an indirect question, which is a construction that starts with a question word (like where) (or if or whether) and takes the same word order as a statement (she lives).