Is this a good Lucina Build?

That's a decent build. But since she has Fury I would replace Seal Spd 3 with Desperation or even Wrath since the damage after combat syncs really well. As for C skill, it's flexible but I personally prefer Hones because it's great for offensive units. For the Seal, I recommended Heavy Blade since your Lucina has a high attack stat and she can charge Aether faster. Although, the healing from Aether might counter Sealed Falchion's effects.

Lucina’s low defenses makes keeping her HP up kinda crucial, because it’s really all she has when she has to take any hits. Because of this, I don’t think running Fury is the best idea. Lucina could go well with Death Blow or Swift Sparrow. If you can’t or don’t want to replace Fury, Aether isn’t exactly the most reliable way to heal bc of its cooldown count, but it could work as long as you make it so it activates quicker. Using the B slot skill Wrath is probably your best bet, but i know you mentioned you don’t have access to it, so you could otherwise equip either Heavy Blade or Quickened Pulse for her S Seal (Heavy Blade is a better option here) and have a teammate of her’s with Infantry Pulse