Peel and core the apples, and cut them into slices about ¼-inch thick. Place the apple slices in a bowl, and add the lemon juice. Stir to coat every slice.
Place a medium saucepan over medium heat. Add the butter. After the butter has completely melted, add the apples and lemon juice. Simmer until most of the liquid has cooked off or been absorbed by the apples, about five to six minutes. Note: The apples should maintain their shape, yet be slightly tender when you pierce them with a fork.
Add the sugars and honey, and stir to combine. Reduce the heat to medium-low and cook an additional minute or two, until the sugar has completely dissolved.
Remove the apples from the heat, and add the cinnamon. Stir one final time, and serve it immediately.