Lucina IVs +atk -res or +spd -def

You're probably better off staying with your +Atk -Res, in my opinion. Lucina's Res is already so low that it's her dump stat. You don't really want her to tank mages in the first place. A bane in Def would mean 22 Def, which is incredibly low for a melee unit. In other words, Lucina would be suffering from a low 22 Def and 19 Res. Overall, it's just better to leave her 25 neutral Def as it is.
It's true that Speed is arguably the better stat to keep up with the likes of Ayra or Karla, but whether you want to sacrifice her Def or not is entirely up to you. You can, however, patch up all her stats with the Bond Falchion refine but it would also require a teammate to always be by her side.

if LnD then go +spd/-def but if fury then go +atk/-res

res bane for her is optimal but in some situations she would prefer the spd

Even with +spd, a handful of sword units can still double Lucina. If she's running Quick Riposte, she can double back but will not prevent getting doubled. Having said that, preserving her Def will help reduce incoming damage, especially when she's expected to get doubled. The +Atk will allow her to hit harder and can win her crucial match ups and since she will double with QR on enemy phase, you'll want to make sure every damage she does counts. Go with the +Atk/-Res. This is especially appealing if you want to give her DC, which already implies enemy phase build.

If you go for a dc build you probably want her bond falchion with qr.
If you are going for a more offensive build you could go with sealed falchion, desperation and the spd ivs

As someone running the famous Lucina Emblem DC build (thank you Ryan on YouTube) with a +Spd/-Res IV spread, I'd still recommend the Atk currently. Spd is her best boon but Res doesn't hurt as much as you'd think as the bane. She can still tank most mages and with a support partner near double back. Just let that partner have either a Hone or Drive Spd to help a bit.

Having DC and the bond refine let's her tank quite a lot and Aether back through it. Just gotta be careful she doesn't take on too much. I'd keep an eye out for +Spd/-Res or HP, but you already have an attachment to and know this current IV spread. She's gonna do just fine for you.

Enjoy her my fellow Lucybro or sis!

Definitely stay with +Atk, not worth such a crappy bane when you have the optimal one with at the lowest second best boon lol