Place strawberries in container of an electric blender; cover and process until smooth, stopping once to scrape down sides. Pour strawberry puree through a wire-mesh strainer into a large freezer-proof container, discarding pulp and seeds. Add lemonade and water to container; stir well. Cover and freeze 4 hours or until slushy.
To serve, transfer lemonade mixture to a large pitcher or a small punch bowl. Stir in mineral water, and serve immediately. Garnish with lemon slices, if desired.