Lion can win through honor because they don't need to rely on honoring their bodies as often as other clans.
Ikoma Prodigy gives you an honor when you recruit her.
Venerable Historian honor's herself when she enters a conflict.
Honored General honors himself when he enters play.
Akodo Gunso has pride so when you win that military conflict you were already going to win he honors.
That is 12 cards in the dynasty deck alone that feed you honor.
On top of these 12, we have the Kitsu Spiritcaller to allow you to trigger some of the effects again. Bringing back an honored general or a venerable historian can net even more honor. So you can just dig through the dynasty deck to gain honor just for using your bodies, and because a lot of it is honored you need the fire ring less and can focus on the air ring.
Then you have fantastic cards to keep the pressure off of you, because you lose honor if you can't defend, so you need chump blockers.
Steadfast Samurai is always there to defend for you.
Keeper Initiates also return every time you win the earth ring, which you might swing for to get that sweet card draw. They can be very good chump blockers when they come back with one fate.
You also have Toturi who can nab the fire/air ring twice when he swings, also an excellent Spiritcaller target.
Then you have Staging Grounds which lets you flip up your face down dynasty cards before the end of the turn, to dig for even more of your honoring characters or to be able to discard them so you make room to dig deeper.
Then in the Conflict deck you have court games to honor on political conflicts and Honored Blade to gain honor when you win those military conflicts you know you want to win.
If you splash phoenix you can use Display of power to steal the air ring from the opponent if they swing first and Seeker of Air to gain access to another courtier and swing for air again. Also Magnificent Kimono to again gain honor from winning conflicts.
Lion Honor has a few natural predators, but its at least feasible as you dig through your dynasty for honor characters, bring them out, swing for air, then defend only to dig for more and resurrect the dead ones to keep the honor train rolling.