Lan Yan

4★

AnemoCatalystShielder

TL;DR

Lan Yan's Skill puts up a shield and dashes her forward. If she connects she bounces into the air, where a Normal Attack throws her rings out for some Anemo damage. Hit an enemy that is already wet, burning, frozen or shocked and the shield takes on that element, which makes it soak that element far better. Her Burst hoovers everything into a pile. One dash a rotation, a shield, plus whatever Viridescent Venerer does for the team.

Rotation

Skill (E) into an enemy carrying Hydro, Pyro, Cryo or Electro. Hold it first if you need to point the dash somewhere. The shield goes up as she casts and picks up that element when the dash lands.
Normal Attack while she is hanging in the air to throw the rings, which bounce twice between nearby enemies.
Burst (Q) to drag the group into one spot for a stack of Anemo hits.
Swap off. The shield holds for 12.5 seconds.

Abilities

Skill (E)	16 second cooldown. Raises the shield for 12.5 seconds, sized off her Attack, then dashes her forward and pops her into the air on contact. Hold to aim the dash. While she is up there, a Normal Attack or another press of the Skill throws her rings at an enemy.
Burst (Q)	60 Energy, 15 second cooldown. Pulls nearby enemies and loose objects towards one point and hits them several times with Anemo.
The shield	Soaks Anemo damage at two and a half times its face value, the same again for whichever element it converted to. The rings pick up that element too, for an extra hit worth half their damage.

The one mechanic to understand

The dash has to land on something that already has an element on it.

The shield comes up whether the dash hits or not. The conversion does not: that only happens when the dash makes contact with an enemy carrying Hydro, Pyro, Cryo or Electro. So she goes in after the teammate who applies the element, not before. What you get for it is a shield that soaks the element actually being thrown at you, plus a second chunk of damage on her rings in that element. Dash into a dry enemy and you still have a shield, just an ordinary one.

What actually matters

The two or three real decisions. Everything else is noise.

Attack. The shield is a percentage of it. It also takes a snapshot on cast, so any attack buffs sitting on her at that moment are baked in for the full 12.5 seconds.
Energy Recharge. The Burst is 60 and you want it every rotation. Favonius Codex or a second Anemo character covers most of it.
The shield is shorter than the cooldown. 12.5 seconds of shield against 16 seconds of cooldown leaves a gap in every rotation. There is nothing to do about that until Constellation 6 gives her a second charge.

Gear

A build that works. KeqingMains lists every other option.

Weapon	Energy Recharge, then Attack. Favonius Codex is a standard banner 4-star that solves the Energy for the whole team. Thrilling Tales of Dragon Slayers instead if her Energy is already fine, since it moves a fat attack buff onto whoever you swap in.
Artifacts	4-piece Viridescent Venerer. Her swirls cut enemy resistance to the swirled element for the whole team, which is worth more than anything her own damage does.
Main stats	Energy Recharge sands, Attack goblet, Attack circlet. Swap the circlet for Crit Rate only if you gave her Favonius Codex and its passive keeps missing.

Works well with

Hydro

Pyro

Electro

Cryo

Those four are the ones the shield can absorb, so they are also the ones that turn her rings into a second element. Hydro and Electro are the easiest to have applied before she dashes.

Don't bother

Her ground attacks, including the Charged Attack that eats 50 stamina a throw.
Chasing Elemental Mastery. It does add to her Skill and Burst damage, which is not what she is in the team for.
Aiming the dash in an ordinary fight. Hold is for when the enemy you want is off to one side.
Her Burst as a damage move. It is there to bunch the enemies up so the rings and the swirls all land on something.

Want the full theorycrafting version? Read Lan Yan on KeqingMains.