Lute

• Preferred IV: +SPD or +ATK / -DEF or -HP
• Weapon: Weirding Tome
• Assist: Draw Back / Rally Spd/Def
• Special: Iceberg / Glacies
• Passive A: Fury 3
• Passive B: Desperation 3 / Windsweep 3
• Passive C: Res Ploy
• Sacred Seal: Atk Ploy / Spd+3

With this build, Lute is able to run Arvis' triple ploy build to an even greater extent than he can- as a matter of fact, this Lute will actually be immune to Arvis and hit him with her own RES/SPD/ATK -5.  With a Fury, her Resistance hits a staggering 37 allowing her to effectively triple ploy the majority of units in the game.

She functions here as the ultimate debuffer, which goes nicely with the fact that she can also hit 53 atk/38 spd unbuffed.  Her low HP works out to her advantage, as it will only take two fury procs to send her into Desperation, provided she takes no damage- if she does take damage, she'll likely hit desperation range after the first combat. Lute can then safely double any unit with comparable speed to her, provided she gets off that handy speed ploy proc from her native tome.

Running triple ploy makes Lute a great damage/support hybrid for your team, as she is capable of debuffing most units in the game to a crippling amount and can set them up for kills from your damage dealers or defensive wins from your tanks. She mitigates threats and makes the baddies easier to take care of. While her low hp makes tanking Moonbow/Quickened Pulse +10 Reinhardt a bit of a risk, she can easily do so if she hits him with Atk Ploy or if she gets a Resistance buff.

Fury is a no-brainer in addition to this, as she could use dramatic improvement to her speed and res and the self-damage inspires Desperation procs.  Desperation works nicely if Lute is capable of securing doubles via debuffing the enemy or receiving buffs herself, however, in a DC heavy meta, Windsweep is also an option that will allow her to safely attack into units like Ryoma, Ayra, Hector, and other units that have inherited DC. 

Rally Spd/Def helps the units that most easily pair with her: red counterparts that need to be able to counter the physical green units that counter her. Finally, Iceberg is a fantastic special to supplement her high res while retaining a low enough proc rate that she's likely to use it throughout your matches.

• Preferred IV: +SPD / -DEF or -HP
• Weapon: Blárblade+
• Assist: Reciprocal Aid
• Special: Moonbow / Iceberg
• Passive A: Life and Death 3
• Passive B: Desperation 3
• Passive C: Res Ploy 
• Sacred Seal: Spd+3

This is the default blue bladetome kit that you have probably seen applied to Mae, Delthea, Linde, Olwen, and now Lute. Due to blue mages having similar stat lines, the set works about the same on all of them, give or take a few points.  In comparison, Lute has the same attack value as Mae and Delthea and she has 1 more Attack than Linde. Conversely, Lute has 1 more Speed than Mae, 4 less Speed than Linde, and 2 less Speed than Delthea.  The tradeoff is that Lute has more Resistance than all of them, with 4 more than Mae, 7 more than Linde, and 3 more than Delthea.

That was a lot of numbers all at once but it basically boils down to this: Attack-wise, Lute is among the best Blarblade users, Speed-wise, she's worse than Linde and Delthea. Resistance-wise though, she's the best and will still be able to function as an anti red mage and still has the option to proc Res Ploy and hit with a moderate Moonbow, despite Life and Death's debuff which takes her down to 29 Resistance.

With all that being said, Lute hits 40 neutral speed with a +SPD IV and Life and Death, giving her 43 Speed with a Seal and 47 Speed if she has a buffer on her team- more than enough to take anyone down with an Attack of 54 and the ability to have her damaged buffed by bladetomes. It's cookie cutter, but it works for a reason.