To prepare artichokes: Fill a Dutch oven or large pot 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. 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/pot and bring to a boil. Boil until the base of the stem can be easily 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 bottom 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.