To prepare artichokes: Fill a Dutch oven with water; add the juice of 1 lemon. Trim leaves from the top of an artichoke. Remove the outer layer(s) of leaves from the stem end and snip all remaining spiky tips from the outer leaves. Trim an inch off the bottom of the stem and use a vegetable peeler to remove the fibrous outer layer. As each artichoke is prepared, drop it into the lemon water to prevent it from turning brown.
When all the artichokes are prepared, cover the pan and bring to a boil. Boil until the base of the stem can be pierced with a fork, 12 to 15 minutes. Transfer to a cutting board and let stand until cool enough to handle, about 10 minutes.
Meanwhile, preheat grill to medium. Slice the artichokes in half lengthwise. Scoop out the choke and first few inner layers in the center until the heart is revealed. Brush each half with oil and sprinkle with salt and pepper. Grill the artichokes until tender and lightly charred, about 5 minutes per side. Transfer to a serving platter, squeeze half a lemon over them and garnish with the remaining lemon half cut into 4 wedges. Serve warm, at room temperature or chilled.