Really, no, she couldn't have. She was far removed from the title; her claim would've gone as far back as possible to being the granddaughter of Finwe himself. Finarfin's house never held the title. This gives her virtually no claim - Elrond was the grandson of Turgon and great grandson of Fingolfin. Additionally, there were very few Noldor left in Middle-earth and those left dwelt in Lindon or Imladris, not Lorien.
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...take counsel with thyself, and remember who and what thou art.
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