Sort and wash beans; place in a large Dutch oven. Cover with water to 2 inches above beans. Cover; let stand 8 hours. Drain.
Heat oil in Dutch oven over medium heat. Add carrot and next 5 ingredients (carrot through celery); sauté 5 minutes. Add beans, 1 1/2 cups broth, chili powder, and next 4 ingredients (chili powder through garlic). Cover; cook 5 minutes. Add remaining 1 1/2 cups broth, rice, lentils, barley, raisins, salt, and pepper; bring to a boil. Reduce heat; simmer 25 minutes. Stir in tomato; set aside.
Warm tortillas according to package directions. Spoon 1 cup bean mixture down the center of each tortilla. Top each with 1 tablespoon cheese and shredded lettuce; roll up. Cut each burrito in half diagonally; place 2 burrito halves on a plate; serve with 1 tablespoon sour cream and 2 tablespoons salsa.
Note: You can substitute two (15-ounce) cans black beans, drained, for 1 cup dried beans and omit step 1, if desired.