Peel, core, and cut the apples into 1/2-inch-thick slices (try a combination of Gala, Golden Delicious, and McIntosh). In a large saucepan, combine apples with the cinnamon stick, sugar, and 3/4 cup water; bring to a boil. Reduce heat; cover, and simmer, stirring occasionally, until apples are tender, 30 to 35 minutes. (If sauce begins to stick to the bottom of the pan, add 2 to 4 tablespoons more water.)
Remove from heat; discard cinnamon stick. Stir in lemon juice.