In a large bowl, mix together the shortening, white sugar and brown sugar until smooth. Stir in the egg and vanilla. Combine the flour, baking soda and salt; stir into the batter until blended. Mix in oats and walnuts. Drop by teaspoonfuls, 1 inch apart, onto greased cookie sheet.
Bake for 12 minutes or until lightly browned. Immediately remove cookies to wire racks and allow to cool.