Trim the artichokes
Grate 1 teaspoon zest from the lemon. Halve the lemon and squeeze 2 teaspoons juice from one half. Reserve both lemon halves. Snap off the tough outer leaves from each artichoke and trim the spiny tops and the stem. Remove any fibrous portions around the base. Halve the artichokes. As you work, rub all the cut areas with the lemon halves.
Cook the artichokes
Bring a large pot of lightly salted water to a boil. Add the 2 lemon halves and the artichokes, reduce the heat to medium, and simmer until the artichoke bases are tender, about 6 minutes. Drain and rinse under cold running water. Discard the lemon halves. Preheat a grill pan over medium heat. In a bowl, toss the artichokes with the olive oil until evenly coated. Season with salt and pepper and toss again. Cook the artichokes, turning occasionally, until grill marks appear, about 10 minutes.
Make the aioli
Meanwhile, in a bowl, whisk together the mayonnaise, garlic, and lemon zest and juice. Transfer the artichokes to a platter and serve with the aioli.