Lords and knights did attempt to attack each other on the battlefield, but this was because for practical reasons, not personal animosity (although personal animosity might well exist). In medieval combat, a lord or king would not simply be standing on his own. He would be surrounded by his personal men and quite possibly be in charge of a large formation of other troops (medieval armies were often divided into three groups called "battles"). When Philip VI attempted to charge the Black Prince's position at the Battle of Crecy, he did not do so out of spite towards the Prince, but because killing the commander of the English vanguard might have helped turn a losing battle around. To draw a crude analogy, think of the way that a marksman in modern combat might shoot at an officer to throw an enemy unit into confusion. Remember also that medieval officers were not only military commanders, but also politically and socially important people. If a leader of a body of men was killed, his troops might decide to leave the field.

I hope this follow-on question is kosher here, but are there fictional representations of European Medieval battles that are considered most accurate/realistic?