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Fact: Lúthien mostly uses her magic through music, as a possible nod to the Ainulindale; the power of this music was enough to move the heart of Mandos himself
Fact: Arwen is often compared to Lúthien in LOTR and the Professor, to the point where it's stated that "in her the likeness of Lúthien walked in Arda once more" or something, not an exact quote
Fact: The Silmarillion does not, as far as I can tell with my bad reading comp. skills, state directly that Elrond never saw Maglor again during the Second and Third ages
Fact: Maglor was also one of the best musicians in Middle-Earth and, given his epithet "the mighty singer" could very well have possessed similar song magic to Lúthien's
Perfectly reasonable conclusion: Maglor drops by Rivendell; finds Arwen, who inherited Lúthien's gift of music; proceeds to become some incomprehensible combination of music tutor, magical teacher and disaster weird uncle to her; and sticks around for her and Elrond. There are emotional father-son reunions. There are inside jokes like "don't let the TWINS near that WATERFALL!!". Neither Maglor nor Arwen ever has to be lonely again. I continue to procrastinate on the fic.