Place sliced nectarines, sugar, cornstarch, and lemon juice in bowl. Toss to coat.
In small bowl, mix oats, flour, brown sugar and sugar. Cut in cold butter with a fork or pastry cutter until it is combined. You may have chunks of butter and that is okay as the butter will melt in the oven.
Place nectarines in 9-inch baking dish. Top with brown sugar oat crumble.
Bake for 24-32 minutes or until crumble is melted and starts to bubble. If the crumble starts to brown too much, cover with foil halfway through the baking time.