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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. Using small knife, cut our choke and prickly small leaves. Place artichoke in lemon water. Repeat with remaining artichokes.
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Bring large pot of salted water to boil. Drain artichokes from lemon water, add to pot and boil until crisp-tender, about 15 minutes. Drain. Transfer artichokes to rack & cool. (Can be prepared 1 day ahead. Cover & refrigerate).
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Prepare barbecue grill to medium high heat. Whisk oil, 1/3 cup lemon juice, and mint in small bowl. Season dressing to taste with salt & 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 the remaining dressing. Serve warm or at room temperature.