But, even that's problematic. A foe that is unconscious and bleeding to death for example. Do you patch him up and take him prisoner? Let him bleed out? After all, the paladin is the one who's stuck pointy metal bits into that foe, so, the paladin would certainly be responsible for his death. Has that target surrendered or not?
No, they haven't surrendered. They've been battered into defeat, and chose not to surrender before that happened. What happens to them is their responsibility. You could choose to heal them, and if they then surrendered you would be responsible for stopping them being killed. You don't have to, though.
And a rule that says you have to commit genocide? All goblins must be killed? That's about as far from Lawful Good as you can possibly be.
Perhaps. It's somewhat arbitrary but that doesn't mean it's not a rule and obeying your god's commands is a Lawful thing to do. That it's Evil is perhaps true, though that depends somewhat on the nature of goblins. If it referred to Evil outsiders, part of whose nature is to be evil, would it still be controversial?