In a large mixing bowl, toss the apples with the lemon juice.

Add the granulated sugar, brown sugar, and cinnamon, then toss to combine.

In a large skillet, melt the butter over medium-high heat. Add the apples and cook, stirring, until the sugar dissolves and the mixture begins to simmer about 2 minutes. Cover, reduce the heat to medium-low, and cook until the apples soften and release most of their juices, about 7 minutes.

In a medium bowl, whisk together the cornstarch and water. Add it to the apples and continue cooking, stirring frequently, for 1 to 2 minutes, until the mixture has thickened. Remove from the heat and let cool completely. Store in an airtight container in the refrigerator for up to 2 days.