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?

Bill initially didn’t know that the lawyer was looking for Lutkins. It was only when the lawyer reached the station and asked Bill about Oliver Lutkins did he come to know about it. The plan of fooling the lawyer was drafted by Bill on the spot. He offered the lawyer some help in finding Oliver Lutkins as he knew that he would be caught otherwise. This would help him make some money as well. He appeared so genuine and friendly that the lawyer couldn’t see through his plans and agreed to take his help.

The trick is a proof of Bill’s (originally Oliver Lutkins) clever and deceiving nature.