Combine the water and juice. Cut off stem of each artichoke to within 1 inch of base; discard stem. Remove bottom leaves and tough outer leaves, leaving tender heart and bottom. Cut each artichoke in half horizontally. Remove fuzzy thistle from bottom with a spoon. Cut each artichoke bottom into quarters; place artichoke quarters in lemon water. Drain.
Place artichoke quarters in a medium saucepan; cover with water. Bring to a boil. Reduce heat; simmer 15 minutes or until tender. Drain.
Heat oil in a large nonstick skillet over medium-high heat. Add artichoke quarters and garlic; sauté 2 minutes. Add mushrooms; cover and cook 2 minutes or until mushrooms are tender, stirring occasionally. Remove from heat, and stir in parsley, salt, and pepper.