Who's legendary weapon should I refine next?

Neph personally, due to my bias.
If you went Luci I'd say do sealed Falchion, works better for her since she's an offensive unit in stat spread

I think Camilla's weapon should be the one you should refine.
I'm gonna assume that she is you're merge project so in the long run Refining Camilla's weapon is better than refining Lucina's and Nephenee's weapon when you won't use them as much.
(unless you're a whale so Dismiss everything mentioned in the second sentence)

In the end you should just refine the weapon of the Waifu you like the most, Personally I would refine Lucina's and Neph's weapons.

Refine the unit you use the most or have fun with the most and if its all 3 used evenly then go based on which units you have trouble the most.

I guess Camilla for the merge project. I think Sealed falchion is stronger than the awakening effect refine btw.

I think camilla is 100% slept on and is a crucial member of mixed emblem that uses armour and horsies, due to being able to guidance and goad fliers, horses and having flier stats of speed, attack and res (being easy plot territory) buuuuut depends on who you use most and who you like the most, lucina has her niche, and neph is insane, but I feel like Camilla is the best investment in more situations

Camilla. Merge projects come first