Peel and slice the peaches, then place them in a mixing bowl. Add granulated sugar, lemon juice, and gently toss to coat evenly. Transfer the peaches to a buttered baking dish, spreading them out in an even layer.
In a separate bowl, combine oats, chopped toasted almonds, light brown sugar, cinnamon, and vanilla extract. Stir until well mixed.
Pour the melted butter over the dry mixture, then use a fork or your fingers to combine until the mixture forms crumbles and clumps that hold together loosely.
Sprinkle the crumble topping evenly over the sliced peaches in the baking dish, covering all the fruit.
Place the dish in a preheated oven at 375°F (190°C) and bake for about 35 to 40 minutes, until the topping is golden brown and bubbling around the edges.
Remove the dish from the oven and let it cool slightly. The topping will set with a crunchy, nutty texture, and the peaches will be tender and juicy underneath.