If that doesn't solve the problem, try reducing the battle size of your armies, which is an option you can find in the performance tab. Restarting your computer or taking a break from gaming and giving it a fresh start from your desktop might solve it. If you continue to have issues with it, try saving the game after the battle, restarting your machine, and then trying again against another territory. You can still run into problems when trying to besiege a territory. However, this may not always be a good solution. While it may not look the best when you play it, these should further improve the performance of the game, ensuring you can keep playing without too much lag. You want to reduce parameters like shadow type, particle effect, terrain quality, environment details, texture filtering, character details, shaders and whatever else you can try.

To solve this type of problem, the first thing to do is to go to Bannerlord and change the graphics settings on your machine. There is a significantly heavier form of lag that increases during this time, and it should almost happen in a massive game like this, where multiple armies fight each other with massive pieces of siege gear throwing themselves against walls. Some players experience issues in Mount and Blade II: Bannerlord when attempting to besiege an opponent's territory.