Stir together peaches, lemon juice, and cinnamon; cover and set aside.
Stir together flour, salt, and baking powder in a large bowl; cut in butter and shortening with a pastry blender until mixture is crumbly. Gradually add milk, stirring just until moistened. Turn dough out onto a lightly floured surface, and knead lightly 3 or 4 times.
Roll dough into a 13- x 10-inch rectangle; spread peach mixture evenly over dough to within 1 inch of edges. Roll up dough, jellyroll fashion, starting at long side; pinch ends to seal. Cut into 8 slices. Place rolls in a greased 13- x 9-inch pan.
Combine sugars and water in a medium saucepan. Cook over medium heat, stirring constantly, 5 minutes or until sugars dissolve. Pour hot sugar mixture over rolls. Bake, uncovered, at 375° for 40 minutes or until lightly browned. Serve rolls and syrup warm with vanilla ice cream.
Tip: To easily slice roll of dough, place a long piece of dental floss or string under dough 1 1/2 inches from end of roll. Cross ends of dental floss over top of roll; slowly pull the ends to cut through the dough.