I did find the 1860 slave schedule for Claiborne Parish just by Googling those words. It is on ancestry.com. It lists 25 slaves for W. Norton or W.A. Norton, but no names of slaves are given, just age, sex, and whether black or mulatto.
In the 1870 census for Claiborne, there is a William Norton, white, age 74, born SC, wife Sarah, 63, b. SC -- two houses away is a Salina Norton, age 65, black, b. Maryland. Don't know if these connect to your Nortons or not. No Lem listed.