John Livesly/Livesley is the person my wife is researching. Unfortunately, there is no place called Catestone that I've found in Derbyshire, and only Catstone Barn near Wirksworth or the place you found near Nottingham that might work.
But, I have now (yesterday!) found John in the 1841 Census living in Disley, Cheshire. His birthplace is given as Mellor, Derbyshire. There is a farm to the south of Mellor on the OS Map called Capstone. John's father came from New Mills. New Mills, Disley, Mellor are all within a few miles of each other, around NW Derbyshire. So, I'm thinking that Catestone must be a transcription or entry error in the 1881 Census.
Many thanks for your help