Heat oil in a large pot over medium-high until shimmering, about 1 minute. Add onion and carrots; cook, stirring occasionally, until softened, 6 to 8 minutes. Stir in garlic, ginger, salt, cumin, turmeric, and pepper; cook until fragrant, about 1 minute.
Stir tomatoes, broth, and lentils into mixture in pot. Bring to a boil over high; reduce heat to low, and stir in coconut milk. Cover and simmer over low, undisturbed, until lentils are cooked through, 25 to 30 minutes. Stir in lime juice and cilantro; season with additional salt to taste. Garnish with additional cilantro; serve with crushed red pepper and lime wedges.
