When you stat replace your king, his heritage always matches the heir's heritage even if you choose to keep the old king's appearance. This doesn't make sense to me, because the only physical a stat-replaced king keeps from the heir is the mutation, which (for the most part) isn't heritable anyway.

So my suggestion is to keep the old king's heritage in place if keeping his appearance when crowning a new king! It seems logical that the record's of the lion's parents should stay consistent with where their markings came from, and it's also more convenient for people who keep track of family lines/have stories about their pride/etc but still want to stat replace.