Heat the oil in a large pot over medium-high heat. Add the onions, carrots, thyme, paprika, and ½ teaspoon each salt and pepper. Cook, stirring often, until the onions are tender, 10 to 12 minutes. Add the broth and 2 cups water and bring to a boil. Reduce heat and simmer, stirring occasionally, until the carrots are soft, 12 to 15 minutes.
Working in batches, puree in a blender until smooth. Stir in the lemon juice.
Serve the soup topped with the yogurt, olive oil, and pepper.