In a large bowl, combine juice of 1 lemon and 6 cups of water. Put the onions, celery, and carrots into the water and set aside.
Cut off the stalks of the artichokes and pull off all the leaves. Dig out and discard the fuzzy center (the choke) from the middle with a spoon. Using a small paring knife, trim into a neat cup shape. Put each one immediately into the water with the other vegetables to prevent them from discoloring.
Take the artichokes out of the water and arrange side by side in a large heavy-duty pot. Strain the other vegetables from the bowl of water and add to the pot. Mix the juice of the remaining lemon with the olive oil, 4 cups of water, and 2 teaspoons of salt; pour over the veggies. Add the thyme, bay leaves, peppercorns, and black pepper, to taste. Cover and cook on low gently for about 30-40 minutes or until the artichokes are tender.
Let cool slightly. Lift the artichokes out of the pot and place them, hollow side up, on a serving platter. Spoon the vegetables into the middle of the artichokes and around them, and garnish with lemon slices and fresh herbs. Serve immediately.