Heat the oven to 350°F (175°C). Lightly grease a 9x9-inch or 2-quart baking dish.
In a large bowl, toss the apple slices with the lemon juice and vanilla. Sprinkle over the granulated sugar, flour, cinnamon, nutmeg and salt, and toss until the apples are evenly coated. Spread the apples in the prepared dish.
In a medium bowl, stir together the oats, flour, brown sugar, cinnamon and salt. Pour in the melted butter and stir with a fork until the mixture forms moist clumps.
Scatter the oat topping evenly over the apples, covering them completely, and press it down very lightly.
Bake for 35 to 45 minutes (about 40 minutes), until the topping is deep golden and crisp and the apple juices are bubbling thickly around the edges.
Rest for at least 15 minutes so the juices thicken slightly. Serve warm, with vanilla ice cream if you like.