Add apples, 2 tablespoons water, lemon juice, maple syrup and cinnamon (if using) to a high-speed blender and puree, adding more water if needed to achieve desired consistency.
For raw sauce, pour into a bowl and serve or chill (must be consumed the same day).
For cooked sauce, transfer mixture to a saucepan and simmer over medium-high heat for 1-2 minutes. Serve warm or chilled and store in the refrigerator for up to 3 days.