Good way to get feathers without arena?

Tempest Trials, Missions, Voting Gauntlet and Chain Challenges
Those are the only way possible to besides Arena and HM, I think

Slap a Speed +1 seal on your own neutral speed Brave Lyn, and she'll double and kill any Brave Lyns with neutral speed because of swift sparrow (everyone and their cat picked B!Lyn for their free summon so most are neutral). As for feathers, there's the ongoing TT, chain challenges (both of course would help with grinding HM as well as SP) and sending home heroes you definitely won't use.

Alternatively, try only going for the lower tiers. You won't get as many feathers but some is better than none.

You might feel motivated after only a week or so break, but you could start thinking of ways to hard counter her. Here are a few tips:

- Panic Ploy. Brave Lyn is easy to beat out with HP, so panic ploy can turn Hone Cavalry into penalty.

-Atk Ploy 1 seal. Nearly all Lyns are sporting a brave bow right now, so crippling her attack will be a huge help.

-Bowbreaker. With bowbreaker, you can stop a brave bow brave Lyn from quading and thus releasing her special. A unit with half way decent defense will survive.

-Guard. If you have somthing like Lukas, Guard can allow Lyn to quad and not release her special (this is my main solution.)

- Distant Def 1 seal. Adds a 2 more points to defense from ranged attacks, saves 8 damage from a quad.

- Brave Ike. Urvan's passive will make consecutive arrows bounce off him if you manage to pull him. Beorc's blessing will also
Negate buffs on cavalry units.

- Raven tomes. Most Lyns do not have cancel affinity, so you should be safe to run triangle adept. An even safer option might just be to pick a mage with good defense.

Otherwise, grinding TT and Voting Gauntets are probably your best bet for feathers.