Cover mushrooms with warm water in a small bowl. Let stand for 30 minutes. Strain, reserving liquid. Rinse the mushrooms well under cold water; drain and chop. Strain the reserved liquid through a coffee filter or paper towel to remove any dirt.
Meanwhile, fill a large bowl with water; juice the lemon and, reserving half the juice, add the rest along with the lemon halves to the water. Pull off outer leaves from an artichoke. Using a small, sharp knife, pare the artichoke down to the heart. Trim the bottom of the stem, then peel the stem. Scrape out the choke with a melon baller or spoon. Cut the heart into quarters and place in the lemon water to prevent browning. Repeat with the remaining artichokes.
Heat oil in a large deep skillet or Dutch oven over medium heat. Add leeks, carrots, garlic, thyme, mushrooms and the artichoke hearts; cook, stirring often, until the vegetables start to brown, about 5 minutes. Add wine and cook until slightly reduced, 2 to 3 minutes. Add broth, salt and the reserved mushroom liquid. Cover and cook over low heat until the artichoke hearts and carrots are almost tender, 30 to 40 minutes.
Stir in lima beans and peas. Increase heat to medium, cover and cook for 10 minutes more. Stir in butter and the reserved lemon juice. Season with pepper. Serve the stew in shallow bowls, garnished with chives and parsley.