1. Coarsely chop lemon, including peel and rind; discard seeds. Place lemon and dates in a food processor; whirl until evenly chopped. Add 3/4 cup sugar, the butter, and egg; whirl until blended and the lemon and dates are finely chopped.
2. In a bowl, mix flour, baking soda, and salt. Add to date mixture; whirl until blended. Stir in walnuts. Spread batter into a buttered and floured 4- by 8-inch glass loaf pan. Bake in a 325° oven until a toothpick inserted in center of thickest part comes out clean, about 1 hour.
3. Meanwhile, in a 1- to 1 1/2-quart pan, combine remaining 1/2 cup sugar and lemon juice. Stir over medium heat until sugar dissolves, about 2 minutes.
4. When bread is done, use a long, thin skewer to make holes about 1/2 inch apart all over surface. Pour hot syrup evenly over hot bread in pan. Let stand at room temperature until bread absorbs all syrup, about 2 hours. Turn out of pan onto plate. Cover airtight; chill overnight or up to 3 days. Thinly slice to serve. Chill leftover bread airtight.