Tolkien once got a letter like this and said that she was not the inncarnation of Luthien. Luthien was turned from and Elf to a Woman and when she died her spirit left Middle-Earth and never returned. Arwen therefore can't be her spirit in another form as Luthien is long gone, her spirit far from Middle-Earth. However Tolkien did say that they were extremly similar and shared a similar fate. They even looked so alike that when Aragorn first saw Arwen he called to her with the name Luthien.
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