Fill a medium bowl with water and squeeze the juice of 1 lemon in the bowl, tossing in the lemon halves as well. Rinse each artichoke and trim 1/2-inch off of the stalk. Trim 1-inch off the top of each artichoke. Then cut each artichoke in half, from stalk to tip, and remove the choke with a spoon. Remove the tough outer leaves and trim the outside of the stalk with a paring knife. Add the prepped artichokes to the bowl of lemon water to keep from browning.
Slice the remaining lemon. In a baking dish large enough to place the artichokes in 1 even layer, place the slices in the dish to form a bed for the artichokes. In the center of each artichoke, add a garlic half and drizzle with half the olive oil. Sprinkle with salt and pepper, then place cut side down on top of the lemon slices. Pour the chicken stock around the sides, drizzle the remaining olive oil over the tops of the artichokes, sprinkle with salt and pepper, cover and firmly seal with aluminum foil. Bake in the oven until fork-tender and the leaves peel off easily, about 1 hour.