|Brave Lyn's base kit is already so synergistic out of the box that building her should basically be a no-brainer. With just a minimal amount of Skill Inheritance, the defaults resemble near-perfection and don't require you to break your bank or feathers. As a significant number of players chose Lyn as their free 5 star from the banner, and Lyn's base stats are already very good, this set absolutely works with the default neutral statline. If you pulled a +Atk or +Spd version, however, those should be utilized unless the accompanying bane interferes with either stat. Resistance should be untouched as it preserves her bow's anti-mage capabilities.
Mulagir grants Lyn a free 3 points to her Speed (effectively giving her an extra boon to the stat), and thanks to its other effect, enables her to tank and break through the ever-oppressive roster of Bladetome sweepers, especially Cecilia, Olwen, and Linde. It is also legendary, which slightly boosts Arena scores. Overall, there's little need to replace her weapon. With the provided boosts from Lyn's default Swift Sparrow 2, the Brave Lady becomes ridiculously powerful and, more importantly, faster than most standard threats can handle.
The rest of her moveset is simply a flexible multiple choice.
For her assist, Reposition and Draw Back are good assist skills that allow Lyn to save her teammates from difficult positions.
Special-wise, Draconic Aura comes with Lyn's base set and works consistently off her great Attack, though Luna has the potential to sting high-Defense threats more easily.
For the B-slot, there are many choices: Sacae's Blessing basically invalidates physical melee units who can counter at a distance on Lyn's turn, giving her the opportunity to safely KO these units such as Ryoma, Hector and other Distant Counter units. If you have those threats covered, however, Desperation 3 most certainly is an option to score safe KOes in single skirmishes after Lyn reaches the HP threshold and also works extremely well on Lyn given her speed. Cancel Affinity 3 easily deals with any Raven tome users that are employed as countermeasures to colorless attackers. A weapon breaker of your choice can also be used depending on threats your team has trouble with, though the aforementioned B passives deal with all threats to a general degree.
Atk Smoke 3 is basically Seal Atk 3 on a less compromising passive slot (many units would love to run it, but they need more useful B slots instead) and could present interesting defensive applications when positioned correctly. Lyn can also utilize a cavalry boost to support fellow cavalry units if placed on a horse emblem team. Needless to say, Lyn benefits from Hone Cavalry herself as the Speed boost in particular basically makes it impossible to outmatch her, and she isn't hurting for more Attack boosts either. On other team compositions, regular Hone Atk 3 and Hone Spd 3 support will, of course, suffice.