Trim the tops from the artichokes, then cut in half lengthwise, and place halves into the bowl of lemon water to prevent them from turning brown. Bring a large pot of water to a boil. Meanwhile, preheat an outdoor grill for medium-high heat. Add artichokes to boiling water, and cook for about 15 minutes. Drain. Squeeze the remaining lemon wedges into a medium bowl. Stir in the olive oil and garlic, and season with salt and pepper. Brush the artichokes with a coating of the garlic dip, and place them on the preheated grill. Grill the artichokes for 5 to 10 minutes, basting with dip and turning frequently, until the tips are a little charred. Serve immediately with the remaining dip.