In saucepan, combine water and sugar. Cook over medium heat until sugar dissolves. Pour into 13x9x2-inch glass baking dish. Add lemon juice; stir.
Purée 1/2 cup strawberries and 1/2 cup raspberries in food processor or blender; add to lemon mixture, mix well. Stir in milk,* cover with plastic wrap; freeze 15 minutes. Remove from freezer and scrape ice crystals with spoon. Return to freezer for 15 minutes; remove and scrape ice crystals. Continue this process, scraping every 15 minutes until mixture reaches desired thickness, about 1 hour.
Divide remaining berries among 4 glasses. Add 1/2 cup soda, top with slushy mixture. Stir slightly; serve immediately.
*Don’t be alarmed if milk curdles slightly.