Preheat oven to 450 degrees. Spread pecans in a 13-by-9-inch baking dish; toast until fragrant, 3 to 5 minutes. Remove pecans, and set aside (or store in a resealable plastic bag, up to 1 day).
In a large bowl, combine sugar, lemon juice, and 1/4 cup water. One at a time (to prevent them from turning brown), halve apples through the stem end, core, using a melon baller, and immediately toss with sugar mixture.
Arrange apples, cut side down, in baking dish; pour sugar mixture over. Tuck in cinnamon sticks; cover dish with foil. Bake until apples are easily pierced with the tip of a paring knife, 15 to 20 minutes.
Serve apples with ice cream, topped with pan juices and pecans. Garnish with cinnamon sticks, if desired.