Melt the stick of butter in a large skillet over medium heat. Add the apple slices and lemon juice (try to get a little lemon juice on each slice) and cook for 2-3 minutes.
Stir in both sugars and cook for another 5-8 minutes, depending on how thick your slices are. You want the apples soft, but not mushy.
In a small bowl, combine the water and corn starch. Add into the apple mixture and cook for 1-2 minutes to allow the sauce to thicken.
Serve warm (it is amazing with a little vanilla ice cream!)