Place beets into a 9x13 inch baking dish. Drizzle with 2 tablespoons olive oil and lemon juice. Season with salt and pepper to taste.
Cook beets in preheated oven, turning occasionally, until fork tender, about 45 minutes. Remove from oven, cool, peel, and cut into 1/2 inch pieces.
Heat 2 tablespoons olive oil in a large pot over medium heat. Stir in the onion, garlic, celery, and mushrooms; cook and stir until the onion becomes transparent, about 5 minutes. Pour in the chicken broth, and heat 5 minutes. Add the lima beans and mixed vegetables; bring soup to a boil over high heat. Reduce heat to medium-low, and stir in the tomatoes, peas, beets, and crab meat. Season with thyme, hot sauce, salt, and pepper, to taste. Simmer 10 minutes more, and turn off the heat. Just before serving, stir in 2 teaspoons lemon juice.