I would give 2 chances of death.
One from execution after being captured. Very rare for the AI.
Another would be that in battle when a lord or companion dies (they still get red skull) they get a wound. When they have a wound they won't join any army and will be very cautious for attacking small groups, will tend to stay defending their own fiefs until they recovered. Recovery time could be something like the triple of recovering standard health. When lord die in this condition the relation loss would be smaller. They could also die in their moment of triumph winning a battle.