Cut off the top of the artichokes and peel off a few leaves to get to the more tender ones. Trim off the stems and split in half lengthwise. Juice the lemon into a bowl of water and add the trimmed artichokes.
In a bowl, toss together the artichokes, olive oil and salt and pepper. Place the artichokes on the hot grill and cook for 10 minutes. Flip them and cook for an additional 5 minutes. Remove from the grill.
In another bowl, mix together the mayonnaise, chipotle and Parmesan cheese.