In a large bowl, toss the apple slices with 1/2 cup of sugar, 1 teaspoon of ground cinnamon, and lemon juice until well coated.
In a separate bowl, combine the flour and cold butter. Use your fingers or a pastry cutter to blend the mixture until it resembles coarse crumbs.
Preheat your oven to 375°F (190°C).
Spread the apple mixture evenly in a baking dish.
Sprinkle the flour-butter mixture evenly over the apples.
In a small bowl, mix together the remaining 1/4 cup of granulated sugar and 1/4 teaspoon of ground cinnamon.
Sprinkle this mixture over the top of the apple mixture.
Bake in the preheated oven for 30-40 minutes, or until the apples are tender and the topping is golden brown.
Allow to cool slightly before serving. Enjoy warm or at room temperature, optionally with a scoop of vanilla ice cream or a dollop of whipped cream.
Enjoy your meal!