I think here "doom" may just be used in the old-fashioned sense, meaning fate. As in the early middle ages, when it was possible to compile "The Doomsday Book" without the name having sinister connotations. As for the central question, I'd always thought just that Galadriel was Celeborn's treasure and Arwen was Aragorn's, but could easily be wrong about that.
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Father, dear Father, if you see fit, We'll send my love to college for one year yet
Tie blue ribbons all about his head, To let the ladies know that he's married.
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