Combine broth, beans, lentils, 1 cup water, onion, carrot, Parmesan rind, garlic, thyme, pepper, salt, and bay leaf in a 5- to 6-quart slow cooker. Cover and cook on low until lentils are tender, 7 to 8 hours.
Stir in chard and lemon juice. Cover and cook on low until chard is wilted, about 30 minutes. Remove and discard cheese rind and bay leaf.
Divide soup evenly among 6 bowls. Sprinkle evenly with Parmesan.