Preheat the oven to 400 degrees F (200 degrees C). Toss Brussels sprouts, new potatoes, purple potatoes, sweet potatoes, cauliflower, juice from 1/2 a lemon, olive oil, vinegar, mustard, garlic, salt, and pepper together in a separate container. Place on a sheet pan. Cover with aluminum foil. Bake in the preheated oven, flipping vegetables halfway, until sprouts and potatoes are tender and crispy, about 40 minutes. Mix tahini, yeast, 3 tablespoons lemon juice, and water together in a bowl. Add more water to achieved desired thickness. Serve the vegetable mixture in bowls and drizzle the tahini sauce on top.