Heat a large nonstick skillet over medium heat. Add the spinach in batches, turning frequently until wilted (about 7 minutes). Drain spinach (it should be neither wet nor dry, but moist). Combine spinach and garlic in a medium bowl.
Combine water and lemon juice. Working with 1 artichoke at a time, cut off stem to within 1 inch of base; peel stem. Remove the bottom leaves and tough outer leaves, leaving the tender heart and bottom. Cut artichoke in half lengthwise. Remove fuzzy thistle from bottom with a spoon. Thinly slice artichoke heart; place in lemon water. Repeat procedure with remaining artichokes. Drain. (You should have about 4 cups sliced artichokes.) Sprinkle artichokes with salt and pepper.
Preheat oven to 375°.
Arrange 3 cups artichoke in an 11 x 7-inch baking dish coated with cooking spray. Sprinkle with 1/2 cup cheese. Repeat layers with artichoke and spinach.
Cover and bake at 375° for 15 minutes. Uncover and bake 30 minutes. Sprinkle with 3/4 cup cheese. Bake an additional 10 minutes or until artichokes are tender.