Preheat oven to 350° F. Combine apples, lemon juice and 1/3 cup brown sugar. Arrange in buttered 8 or 9-inch square pan. Combine dry ingredients and cut in butter until mixture is crumbly; gently mix in cheese. Sprinkle evenly over apple mixture.
Bake for 25 to 30 minutes. Serve with ice cream or whipped cream, garnish with shredded cheese.