Okay, I'll try and make this as easy to understand as possible. Especially for our non-english speaking friends out there.
1) Execution - Just like it sounds, I think that this game is seriously lacking in ways of player to player execution. It would be a great tool for landowners, lords and any of the noble class to use on the subjects of their realm. Some ideas would be a simple animation of someone leaning over on their knees and you are free to swing your sword at their head. Others could include actual execution style equipment. Things like hanging people with rope, or cutting off their head.
2) Restraints - Before you can execute anyone, you need to be able to capture and restrain them. I will be honest, I've thought long and hard about this feature and I think the only fair way to implement it into Life is Feudal is if you can only capture trespassers or people you have declared war on, script wise. You'd also need a specific item to tie their hands, something like rope or chain links. This would allow you to arrest people, search their inventory and finally execute them.
3) Torture - My final suggestion, torture could be used a tool of punishment for players who are caught by the law or enemy. My vision for this feature would be that torturing people, using various medieval methods, would destroy their skills in the same way dying does. This would be something you could only do to trespassers and enemies. It could be even be used in role-play clans(like my own) and many others around the server.
Some food for thought, please feel free to criticize and add your own ideas!