Combine lentils, tomatoes, broth, onion, carrot, celery, garlic, oil, oregano, thyme, salt, and pepper in a 6-quart slow cooker.
Cover; cook on low 7 to 8 hours until lentils are tender. Stir once after 6 hours; check a few grains before proceeding.
Stir in walnuts and balsamic vinegar; keep covered on warm while pasta cooks.
Boil spaghetti in a large pot according to package directions until just tender, about 9 to 11 minutes. Reserve 1/2 cup cooking water; drain.
Toss spaghetti with lentil sauce. Add reserved water a tablespoon at a time only if needed to loosen.
Divide among 6 bowls, distributing lentils and walnuts evenly.