Well I have found out one thing. John Mills was NOT a lodger. He was the son. It was just a mistake.
When I looked up the marriages for James Mills and for John Mills they both had William Mills Fustian cutter as father. Because there were three lodgers listed directly underneath in the 1871 census it looks as if the word lodger was just written once too often.
So the two who were in trouble with the law were brothers.
Onward......