Matthis

Weapon: Vulture Lance+ (+Def)

Assist: Positional Assist 

Special: Bonfire / Ignis

Passive A: Atk/Def Catch / Atk/Def Solo / Sturdy Stance 3 / Distant Foil 

Passive B: Lull Atk/Def / A/D Near Trace / Mystic Boost 4 / Chill Def/Res 3 / Chill Atk/Def 2 / Quick Riposte

Passive C: Atk/Def Menace

Sacred Seal: Atk/Def Catch / Atk/Def Solo / Quick Riposte 

• Using and improving on Matthis's intended use and skillset isn't such a bad idea, as Vulture weapons offer huge stat returns when fighting against appropriately debuffed enemies. Therefore, leveraging Matthis's strongest stats —that is, Atk/Def —  in combination with Vulture Lance and the synergistic debuffs from Atk/Def Menace make for a solid melee tanking unit. 
• In the B-slot:
  • Ideally, you should distribute debuffs through outsourced methods so that Matthis doesn't have to do it himself with exception to setting up Menace. Though, running double Chill skills such as Chill Def/Res 3 or Matthis's native Chill Atk/Def 2 makes it so that he's not reliant on Menace's four-space range while providing remote support for other allies.
  • If you have penalty spreading covered, conventional defensive passives like Lull Atk/Def, Mystic Boost, A/D Near Trace, or Quick Riposte will aid significantly in Matthis's own combat by tanking enemies and staying around longer with their respective effects. 
• Strengthening Matthis's defensive prowess even further is a natural course of action; this is achieved easily by taking any of the appropriate, listed Atk/Def-flavored passives in the A-slot and Seal. As Vulture Lance requires Matthis to distance himself from allies, though, nearness-based passives such as Unity or Form are definitely not optimal here.

Weapon: Rein Lance+ (+Spd) / Brave Lance+ / Ninja Yari+ / Ninja Naginata+

Assist: Positional Assist 

Special: Bonfire / Galeforce

Passive A: Surge Sparrow / Death Blow 4 / Atk/Spd Clash / Atk/Spd Catch / Atk/Spd Push / Swift Sparrow 3 / Atk/Spd Menace / Other Initiation-friendly Atk skills

Passive B: S/D Near Trace / Flow Refresh / Lull Atk/Spd / Lull Spd/Def / Lull Atk/Def / Flow Guard / A/S Near Trace / A/D Near Trace / Seal Def 4

Passive C: Atk/Spd Menace / Spd Smoke 4 / Def/Res Smoke / Rouse Atk/Spd / Atk/Def Menace / Other Smokes or non-Res based Menaces 

Sacred Seal: Atk/Spd Solo / Heavy Blade / Blade Session / Death Blow

• Matthis does have a more than respectable 43 Atk, which often makes an initiation-based playstyle rather tempting over enemy phase duties. With a great selection of low-rarity inheritable lances, he's perfectly up for the job. Keep in mind that you're effectively ripping off Brave Eirika / Brave Chrom's style, though, and they basically do the job better at low merges.
• The build generally comes in two flavors: you can focus entirely on simply building up Matthis's Atk for a kamikaze-style Brave nuke, or run Spd investment for a generally more stable Matthis that's less vulnerable to follow-ups while making many of his own. The skill choices between the two types of builds are distinct but obvious:
  • For Spd-invested builds, your weapon choice of Rein Lance, Ninja Yari, or Ninja Naginata should be accompanied with additional Spd passives as Matthis's 32 Spd is buildable but definitely not the best. There's a large variety of these in the A-slot and Sacred Seal pool, and a Spd-based Lull (to shut down increasingly common enemy buffs) or Near Trace (for post-combat escape options) will sweeten the deal in the B-slot — through Flow skills are at your disposal to maintain Matthis's follow-up versus Wary effects. Finish off with a Spd-based Menace, Rouse, or Smoke in the C-slot to strengthen Matthis's combat. 
  • The Brave Lance build is less picky and more simple: you forsake his Spd for pure damage-increasing passives like Death Blow and a Def-based Lull, Near Trace, or Seal 4 to significantly strengthen the lance's double strikes. Atk/Def Menace generally gives you the best damage differential possible in a C-slot, but that slot is otherwise flexible.