Squeeze juice from halved lemons into large bowl filled with cold water. Cut stem off 1 artichoke, leaving about 1 inch. Snap off outer 2 rows of leaves. Cut off top 1/3 of artichoke. Quarter artichoke lengthwise. Using small knife, cut out choke and prickly small leaves. Place artichoke in lemon water. Repeat with remaining artichokes.

Bring large pot of salted water to boil. Drain artichokes, add to pot, and boil until crisp tender, about 15 minutes. Drain. Transfer artichokes to rack and cool. Can be prepared 1 day ahead. Cover and refrigerate.

Mix butter and garlic in a small bowl, season with salt and pepper. Set aside.

Prepare barbecue medium high heat. Whisk oil and lemon juice in small bowl. Season dressing to taste with salt and pepper. Brush artichokes with dressing. Grill until tender and lightly charred in spots, turning occasionally, about 8 minutes. Transfer artichokes to platter. Drizzle with some of remaining dressing. Serve warm or at room temperature with garlic butter.

Enjoy.