Preheat oven to 350 degrees. In a large bowl, combine sliced peaches with lemon juice, cane sugar, flour, cinnamon, and salt. Stir gently until the peaches are evenly coated. Pour the mixture into a greased baking dish and spread it into an even layer.
In a separate bowl, mix flour, brown sugar, cinnamon, and salt.
Add the cold diced butter. Use a fork or pastry cutter to cut the butter into the dry ingredients until the mixture is crumbly with small chunks of butter.
Stir in the oats and sourdough discard until just combined. The topping should be thick and a little sticky in texture.
Sprinkle the topping evenly over the peach filling. Place the baking dish in a 350-degree oven and bake for 50-60 minutes. The topping should be golden, and the filling should be bubbling at the edges. If using a larger dish, make sure to reduce the time.
Allow the crisp to cool for 10 to 15 minutes before serving. This gives the filling time to set. Serve on its own or with a scoop of vanilla ice cream.