Prepare a medium-hot charcoal fire. Using a serrated-blade knife, halve artichokes lengthwise. Rub cut surfaces with half of the lemon. Transfer artichokes to a bowl and drizzle with 2 tbsp. oil. Season with salt and toss to coat. Transfer artichokes cut side down to the grill (alternatively, broil artichokes on a baking sheet placed in the middle of the oven). Cook, flipping once, until the bases of the artichokes are tender and the exterior is browned.
Using tongs, transfer artichokes to 2 plates. Drizzle artichokes with remaining oil and the juice of the remaining lemon half. Season with salt. Discard the first layer of leaves before eating, if you like.