The core of that idea always feels more like an examination of misplaced loyalty than pure rivalry. Naruto and Lucy as siblings in a modern AU? Sure, a surface-level setup might have them squabbling over the remote or who gets the last pancake, but the deeper narrative tension I look for comes from their canonical parallels—both are vessels for immense, destructive power (Kurama and the Celestial Spirit King, maybe?), both carry the legacy of a parent they never truly knew, and both are ostracized for what they contain. Their rivalry wouldn't be about who's stronger in a fight; it's about who their father, the Fourth Hokage, would have been prouder of, or who is better living up to the 'Will of Fire' versus the 'Will of the Stars.'
I stumbled across a story once that flipped the script completely. It had Lucy growing up in Konoha, but she was the 'perfect' one—mastering sealing techniques early, a model ninja—while Naruto remained the village pariah. The rivalry was entirely one-sided, fueled by Naruto's bitter envy and Lucy's desperate, failed attempts to bridge the gap, which only made him resent her more. It was less about battles and more about that suffocating dynamic where one sibling's success is the other's constant reminder of failure. The magic versus chakra element was almost secondary.
That's the kind of take I find compelling. The best fics using this premise dig into the psychology of it: how would Naruto's drive to be acknowledged shift if the person getting all the acknowledgment he craves is living under the same roof, sharing his last name? It reframes his entire motivation. The fights, when they happen, are brutal and emotional, less taijutsu spars and more about years of built-up frustration over who gets to claim their father's legacy.