Heat 3 tablespoons olive oil in a large pot over medium-high heat. Add onion and garlic; cook, stirring occasionally, until onion turn golden brown, about 5 minutes. Stir in tomato paste, cumin, kosher salt, black pepper, and 1/8 teaspoon chili powder. Cook and stir until spices are fragrant, about 2 minutes.

Stir in chicken broth, lentils, and carrot. Increase the heat to high and bring to a boil. Reduce the heat to medium-low, cover, and simmer until lentils are soft, about 30 minutes.

Working in batches, fill a blender halfway with soup. Cover and hold the lid down with a potholder; pulse a few times before leaving on to blend. Pour into a pot. Repeat with the remaining soup. Alternately, you can use a stick blender and purée the soup right in the cooking pot. Do not purée all of the soup; leave it a little chunky.

Stir in lemon juice and cilantro, then season to taste with salt. Drizzle with olive oil, sprinkle with chili powder, and serve.