Process chopped persimmon in a food processor until smooth, stopping once to scrape down sides. Measure 1 cup pulp.
Combine pulp, sugar, oil, and egg, stirring until mixture is smooth.
Combine flour, soda, and cinnamon in a large bowl; add persimmon mixture, stirring until blended. Stir in raisins and walnuts.
Drop dough by rounded teaspoonfuls onto lightly greased baking sheets.
Bake at 375° for 9 minutes. Transfer to wire racks placed on wax paper.
Combine powdered sugar and lemon juice, stirring until smooth; drizzle over warm cookies. Cool.