Wash, peel, core, and chop the apples into even ½ inch pieces. Toss immediately with the lemon juice to prevent browning.
In a small bowl, combine the rolled oats, flour, brown sugar, cinnamon, and salt. Drizzle in the melted butter and stir until clumpy and evenly moistened. Add the nuts if using, then set aside.
Melt 2 tablespoons butter in a large skillet over medium heat. Add the apples, brown sugar, granulated sugar, cinnamon, vanilla, and salt, and stir to coat evenly. Cover and cook for 8 to 12 minutes, stirring occasionally, until the apples soften but still hold some bite. For a thicker sauce, stir in the cornstarch slurry during the last 2 to 3 minutes and cook until glossy.
Reduce the heat to low and sprinkle the oat topping evenly over the apples. Cover and cook 3 to 5 minutes more until the topping warms through. For extra crunch, uncover and cook 1 to 2 minutes while stirring gently, or toast the topping separately in a dry pan before adding it.
Remove from heat and let the crisp rest for 5 minutes to allow the sauce to thicken. Serve warm with vanilla ice cream, whipped cream, or yogurt.