I think there should be a mechanism for lords to escape from battle.
Lord AI could be smarter during battles and it could be based on lord personality. Once a lord sees the battle is going south, the lord starts fleeing from the battle and if they reach the edge, they get away. Lords could also keep a small group of elite cavalry by their side at all times to help aide in this escape process. Currently the lords all seem to behave the same way - just chilling in the middle of their troop blob and charging nearby enemies.
This would probably need some thought when lords are facing overwhelming odds - for example, your party of 200 horse archers has chased down their little party of 50 empire recruits. In this case, the enemy lord should attempt to flee immediately (unless they are a headstrong idiot) but the map should be large enough (or the parties start close enough to each other) that the player has a chance to run down the enemy lord before they can escape from the map. This would make it beneficial for the player to have a super fast horse and high riding skill to improve the chances of catching and downing the fleeing lord.
Currently with battles resulting in a capture/kill of a lord 100% of the time, downing a lord in battle just feels insignificant. And because of the snowball problem, the options after battle are all terrible.
1. Release them, they come back the next day with a new army.
2. Capture them. They escape the next day, and are back the next with a new army.
3. Execute them, watch 5 straight minutes of relation loss notifications, and ruin your chances for recruitment the rest of the game.
If it was harder to catch lords, then we could have more permanent options after they are actually caught. Capturing them should be more permanent, and placement in a dungeon even more permanent. And please - just let us execute with smaller penalties. Surely the whole world can't have that big of a problem with some lord they never met on the other side of the world having his head lopped off?