When the lawyer reached New Mullion, did ‘Bill’ know that he was looking for Lutkins? When do you think Bill came up with his plan for fooling the lawyer?
It is more likely that Oliver made the plan to fool the lawyer right after he came to know from the latter that he was looking for a man named Oliver Lutkins. Oliver knew that he was needed as a witness in a law case. So it is entirely possible that he was prepared for such a situation. It was a matter of chance that the lawyer ran into Oliver himself.