|Besides her good stat distribution for the role of a magekiller, Lyn has unique advantages in her bow ignoring mage buffs and being a cavalry unit, which we aim to exploit to provide Cavalry Emblem with a new niche toy - an enemy phase mage killer that crushes all nuke (bladetome and Reinhardt) mages, reducing the dependency on player phasing everything. Using the build is simple: give Lyn the cav buffs/ally support if she needs them and plonk her down in range of enemy mages.
As a mage baitkiller, Lyn obviously does not need def, and any of atk, res or even hp (which is a +4 boon) is suitable, although attack provides unique benefits as we will see later. Fury 3 and Cancel Affinity 3 are logical choices - the first gives her attack and resistance while baiting; Cancel Affinity means she does not have to worry about Triangle Adept 3 raventome carriers.
Being a bow magekiller is a double edged sword: it has no weakness to any 'colour', but on the other hand it is weak to every raven tome in the game. No build is perfect and by nature, some raven mages (Sophia, Cecilia, Boey in particular) who do not carry Triangle Adept and carry Bowbreaker will kill any Lyn build in the game unless she carries the corresponding breaker. The tankier raven/Triangle Adept/bowbreak mages (Sophia, Boey, Robin(M)) will live even a Moonbow retaliation from Lyn, although not killing her due to the effect of Cancel Affinity. However, these builds are by nature rare (particularly the raven/fury builds) on defense and furthermore, can be dealt with by the rest of your (cavalry) team fairly easily given how specialized they are as anti bow units.
Ignoring those particular builds, with the cav buffs Lyn will slaughter most of the 'nuke' mages. We will use the summoner support (SS), cavalry buffs and where necessary, ally support to boost her matchup against the most important edge case, the massively-merged- Quickened Pulse- Moonbow-Bowbreaker Reinhardt.
With Fury and the Summoner Support at S rank, +ATK-DEF Lyn has defensive stats 40 HP / 33 RES and offensive stats 55 ATK / 43 SPD when unbuffed. Draconic Aura backed with Quickened Pulse guarantees the one shot on Reinhardt if you are honed, and rewards you if you one shot a mage hitting into you, leaving you a powerful special for another opponent. Moonbow is an option if the Quickened Pulse seal is not available, and should only be taken with a +atk Lyn - Moonbow backed by a hone cavalry will kill all (neutral hp/def) Reinhardt up to +5, with each additional attack point (from merge or ally support) allowing her to one shot Reinhardts with 2 more merges.
With fortify cavalry on her, 40 hp / 39 res survives a hit from 53 attack Moonbow/Quickened Pulse Reinhardt (up to +8). Any source of at least 2 res or hp (merge, ally support) will be enough to let her live through one hit from even a maxed (+10) Reinhardt - thus the Moonbow build with a distant def seal will comfortably survive any (ungoaded) Reinhardt in the game.
In terms of other options, Iceberg is better on paper compared to native free Draconic Aura by about 1 damage point, so its worth some consideration. G Tomebreaker 3 gives her the ability to beat down some green mages, notably +10 fury Raven Bowbreaker Cecilia and Inigo. Also, Moonbow with the Quickened Pulse seal is an interesting option as it gives you the highest instant retaliation, which ensures the kill on squishy bladetome mages like Nino who might make the switch to Bowbreaker.
Teamwise, the Fortify Res 3 is worth giving to a carrier of Hone Cavalry if you do not wish to run a Fortify Cavalry unit. With a +res IV the resulting buffed Lyn is almost as tanky as the neutral res Lyn with a hone buff. This could then free up a cavalry teammate to use Goad Cavalry, for example.