STEP 1: Preheat the oven to 450°F.
STEP 2: To make the berries: Stir together the strawberries, basil, sugar, and lemon juice in a medium bowl. Let stand at room temperature while you make the biscuits. Just before serving, taste and add more sugar, if desired.
STEP 3: To make the biscuits: Whisk together the flour, sugar, baking powder, baking soda, and salt in a large bowl. Cut in the butter using a pastry blender or 2 knives used scissors-fashion until the mixture resembles coarse crumbs. Make a well in the center of the flour mixture, pour in the buttermilk, and stir with a fork just until a dough begins to form; it will be very sticky.
STEP 4: On a well-floured surface, knead the dough very lightly once or twice with floured hands. Pat out the dough to ¾ inch thick. Dip a 2½-inch biscuit cutter into flour and cut out 8 rounds, reflouring the cutter as needed; gather the scraps together and pat them out again if necessary. Transfer the biscuits to an ungreased baking sheet.
STEP 5: Bake for 12 to 15 minutes, or until light golden brown. Cool slightly on the pan on a wire rack.
STEP 6: To serve, split each biscuit with a fork, and place the bottom halves on 8 serving plates. Spoon a generous portion of the berries over each one, place a scoop of the ice cream and sorbet on the side, and add the tops. Serve immediately.