Bring a large pot of salted water to a boil. Preheat grill to medium-high heat.
Trim the stem from each artichoke to 1 inch long, then bend back and snap off dark outer leaves. Cut top inch of artichokes off with serrated knife. Using a vegetable peeler, peel dark green areas from stem and base of artichoke. Quarter each artichoke. Using a small, sharp knife, cut out the choke and remove the purple, prickly tipped leaves from the center of each wedge.
Place finished artichokes in a large bowl of cold water and squeeze 2 lemons into the water and stir. Continue with remaining artichokes.
Once finished, drain the artichokes and place into boiling water and cook until crisp-tender, about 12 minutes.
Drain the cooked artichokes and place onto preheated grill. Cook until tender and lightly charred in spots, turning occasionally, about 10 minutes.
Meanwhile, in a medium sized bowl, add remaining lemon juice (1/3 cup) parsley, garlic and salt and pepper, to taste. Gradually drizzle in olive oil.
Toss or drizzle the grilled artichokes with the garlic/parsley mixture and serve.