Combine water and 3 tablespoons juice in a bowl. Cut off top 1/2 inch of artichokes. Cut stems to within 1 inch of bases; peel stems. Remove tough outer leaves, leaving tender cores. Halve each lengthwise; add to water.
Drain artichokes; pat dry. Combine artichokes, oil, salt, pepper, and garlic in a bowl; toss to coat. Heat a large ovenproof skillet over high heat. Add half of artichoke mixture to pan; cook 1 minute on each side or until lightly browned. Remove from pan. Repeat procedure with remaining artichoke mixture. Return artichokes to pan; add lemon slices and rosemary. Bake at 425° for 20 minutes, stirring once. Remove rosemary leaves, and sprinkle over artichoke mixture; discard stem and any blackened lemon. Sprinkle with 2 teaspoons lemon juice.
