Whisk Italian and mozzarella cheeses into pan with milk. Stir in juice from half of the lemon. Season with salt and pepper. Adjust heat to low. Meanwhile, add ravioli to pot of water, lower heat, and reduce to a simmer. Cook until al dente, 2-4 minutes. Reserve 1½ cups cooking water, then drain. Stir ravioli, tomatoes, peas, and ¾ cup cooking water into sauce in pan. Simmer until just thickened, 1-2 minutes. Season with salt and pepper.