In a medium sized bowl, mix together flour, brown sugar, 1/4 cup of white sugar, 1/2 teaspoon cinnamon and salt.
Combine butter with flour mixture and cooking oats and mix using a fork until coarse crumbs form. Set aside.
Stir together 1/3 cup sugar, cornstarch and 1/2 teaspoon cinnamon. Place the apples in a slow cooker, stir in the cornstarch mixture; toss with apple cider and lemon juice. Sprinkle the crumb topping on top. Cover and cook on low for 3-4 hours, until apples are tender.