In 1888 Johns Daughter Mary was the ward of William J. Lockerby. He stated her mother was dead and her father hasn't been heard from in over 10 years. So did he leave New Liberty about 1878? He served in the Civil War from August 1861 to December 1864. He listed Residence as New Liberty. He married Evalina in 1866 a couple years after he mustered out .
I found John W. Shaw with wife Evalina and children on the 1870 Census in Smithland Kentucky (Livingston County). His half brother David Weeks is living in the house next door with his family. I also noticed on this census that John marked the box stating that his father was foreign born.
For more information on John W. Shaw click the link below for John W. Shaw's Parents & Updated Fact Sheet.