Morton is a city in Lewis County, Washington, United States. The population was 1,036 at the 2020 census. Morton was first settled in …Morton is a city in Lewis County, Washington, United States. The population was 1,036 at the 2020 census. Morton was first settled in 1871 by James Fletcher. It was later named after Benjamin Harrison's Vice President, Levi P. Morton, in 1889. Morton was officially incorporated on January 7, 1913.