1. Halve and core the McIntosh apples; peel them if you like. Cut each one into 6 wedges.
2. Halve and core the Granny Smith apples; peel them if you like. Cut them into 1-inch chunks.
3. Combine the apples, water, and lemon juice in a deep microwave-safe 2-1/2 quart casserole.
4. Toss the sugar and cinnamon together in a small bowl and stir this into the apple mixture.
5. Microwave, uncovered, at full power for 5 minutes. Stir, pressing the apples into the liquid and return to the microwave. Microwave for another 5 minutes.
6. Using a potato masher, mash the apples, stirring them into the liquid. Allow the applesauce to cool to room temperature, cover, and refrigerate.